Quartz crystal unit, and manufacturing method of the same and manufacturing method of quartz crystal oscillator having quartz crystal unit

ABSTRACT

A quartz crystal unit has a quartz crystal resonator, a case for housing the quartz crystal resonator, and a lid for covering an open end of the case. The quartz crystal resonator comprises a quartz crystal tuning fork resonator capable of vibrating in a flexural mode of an inverse phase and having at least one groove, and an electrode is disposed on at least one of opposite side surfaces of each of the first and second quartz crystal tuning fork tines. The quartz crystal tuning fork resonator has a capacitance ratio r 2  of a second overtone mode of vibration greater than 1500. The lid is connected to the case through a connecting member to cover the open end of the case.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a division of application Ser. No. 11/301,530 filedDec. 13, 2005 and now U.S. Pat. No. 7,412,764, which is acontinuation-in-part of application Ser. No. 10/749,182 filed Dec. 30,2003 and now U.S. Pat. No. 7,071,794, which is a continuation-in-part ofapplication Ser. No. 10/378,719 filed Mar. 4, 2003 and now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a quartz crystal resonator, a quartzcrystal unit having the quartz crystal resonator, a quartz crystaloscillator having the quartz crystal unit, an electronic apparatuscomprising a display portion and the quartz crystal oscillator at least,and their manufacturing methods.

2. Background Information

There are many electronic apparatus comprising a display portion and aquartz crystal oscillator at least. For example, cellular phones,wristwatches, facsimiles and pagers comprising a quartz crystaloscillator are well known. Recently, because of high stability forfrequency, miniaturization and the light weight nature of theseelectronic apparatus, the need for an electronic apparatus comprising asmaller quartz crystal oscillator with a high frequency stability hasarisen. For example, the quartz crystal oscillator with a quartz crystaltuning fork resonator, which is capable of vibrating in a flexural mode,is widely used as a time standard in an electronic apparatus such as thecellular phones, the wristwatches, the facsimiles and the pagers.Similar to this, the same need has also arisen for an electronicapparatus comprising a length-extensional mode quartz crystal resonatorwith a frequency of 1 MHz to 10 MHz to decrease an electric currentconsumption of the electronic apparatus.

Heretofore, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional miniaturized quartz crystal tuning fork resonator, capableof vibrating in a flexural mode, and having a high frequency stability,a small series resistance and a high quality factor. When miniaturized,the conventional quartz crystal tuning fork resonator, capable ofvibrating in a flexural mode, as shown in FIG. 12 (which has electrodeson the obverse faces 203, 207, reverse faces 204, 208 and the four sides205, 206, 209, 210 of each tuning fork tine, as also shown in FIG. 13—across-sectional view of tuning fork tines of FIG. 12), it has a smallerelectromechanical transformation efficiency because the resonator shapeand the electrode construction provide a small electric field (i.e. Exbecomes small), as a result of which the resonator has a low frequencystability, a large series resistance and a reduced quality factor. InFIG. 12, a conventional tuning fork resonator 200 is shown with tines201, 202 and a base 230.

Moreover, for example, Japanese Patent Nos. P56-65517 and P2000-223992Aand International Patent No. WO 00/44092 were published and teachgrooves and electrodes constructed at tuning fork tines of a flexuralmode, tuning fork, quartz crystal resonator. However, they teach nothingabout a quartz crystal oscillator of the present invention having novelshape, novel electrode construction and figure of merit M for a quartzcrystal tuning fork resonator, capable of vibrating in a flexural modeand about a relationship of an amplification circuit and a feedbackcircuit which construct a quartz crystal oscillating circuit.

Additionally, for example, there has been a big problem in theconventional oscillator with the conventional quartz crystal tuning forkresonator, such that a fundamental mode vibration of the resonator jumpsto a second overtone mode vibration by shock or vibration.

Similarly, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional length-extensional mode quartz crystal resonator, capableof vibrating in a length-extensional mode, and having a frequency of 1MHz to 10 MHz, a small series resistance and a high quality factor. Asan example of a length-extensional mode quartz crystal resonator of theprior art, the length-extensional mode resonator comprising avibrational portion, connecting portions and supporting portions, whichis formed from a Z plate perpendicular to z axis, is well known, andthis resonator is formed integrally by a chemical etching process. Also,electrodes are disposed opposite each other on sides of the vibrationalportion formed by the chemical etching process so that the electrodesdisposed opposite each other are of opposite electrical polarity.

Also, a cutting angle of the conventional length-extensional mode quartzcrystal resonator is generally within a range of ZYw(0° to +5°),according to an IEEE notation. In detail, the connecting portions areconnected opposite each other at both end portions of a width of thevibrational portion and at a central portion of the length directionthereof. Namely, the direction of the connecting portions constructedopposite each other corresponds to the direction of the electric field.

When an alternating current (AC) voltage is applied between theelectrodes, an electric field occurs alternately in the width direction,as a result, the resonator is capable of vibrating in the lengthdirection, but the electric field of between the electrodes becomes verysmall because quartz crystal is an anisotropic material and the sides ofthe vibrational portion have a complicated shape formed by the chemicaletching process. Namely, the resonator has small electromechanicaltransformation efficiency because the resonator's shape and theelectrode construction provide a small electric field, consequently, theresonator has a low frequency stability, a large series resistance and areduced quality factor when it has the frequency of 1 MHz to 10 MHz.

It is, therefore, a general object of the present invention to provideembodiments of an electronic apparatus and a quartz crystal oscillator,which constructs an electronic apparatus of the present invention,comprising a quartz crystal oscillating circuit with a flexural mode,quartz crystal tuning fork resonator, capable of vibrating in afundamental mode, and having a high frequency stability, a small seriesresistance and a high quality factor, or embodiments of a quartz crystaloscillator, which also constructs an electronic apparatus of the presentinvention, comprising a quartz crystal oscillating circuit with alength-extensional mode quartz crystal resonator having a frequency of 1MHz to 10 MHz, a small series resistance and a high quality factor,which overcome or at least mitigate one or more of the above problems.

SUMMARY OF THE INVENTION

The present invention relates to a quartz crystal resonator, a quartzcrystal unit having a quartz crystal resonator, a quartz crystaloscillator having a quartz crystal unit, and an electronic apparatuscomprising a display portion and a quartz crystal oscillator at least,and their manufacturing methods. In particular, relates to the quartzcrystal resonator which is a quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode of an inverse phase, and havinga groove and/or a through-hole at tuning fork tines, the quartz crystalunit having the quartz crystal tuning fork resonator, and the quartzcrystal oscillator having the quartz crystal unit. In detail, the quartzcrystal oscillator comprises a quartz crystal oscillating circuit havingan amplification circuit and a feedback circuit, and in particular,relates to a quartz crystal oscillator having a flexural mode, quartzcrystal tuning fork resonator capable of vibrating in a fundamental modeand having an output signal of a high frequency stability for thefundamental mode vibration of the resonator, and also to a quartzcrystal oscillator having a suppressed second overtone mode vibration ofthe flexural mode, quartz crystal tuning fork resonator, in addition,relates to a quartz crystal oscillator comprising a length-extensionalmode quartz crystal resonator. The quartz crystal oscillators are,therefore, available for the electronic apparatus requiring miniaturizedand low priced quartz crystal oscillators with high time accuracy andshock proof.

It is an object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator with a miniature quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,and having a high frequency stability, a small series resistance R₁ anda high quality factor Q₁, whose nominal frequency for a fundamental modevibration is within a range of 10 kHz to 200 kHz.

It is an another object of the present invention to provide anelectronic apparatus comprising a quartz crystal oscillator with aflexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode, and having a high frequency stabilitywhich gives a high time accuracy.

It is a further object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator with alength-extensional mode quartz crystal resonator.

According to one aspect of the present invention, there is provided anelectronic apparatus comprising a display portion and a quartz crystaloscillator at least, and said electronic apparatus having one quartzcrystal oscillator, said one quartz crystal oscillator comprising: aquartz crystal oscillating circuit comprising; an amplification circuitcomprising an amplifier at least and a feedback circuit comprising aquartz crystal resonator and capacitors at least, said quartz crystalresonator being a quartz crystal tuning fork resonator, capable ofvibrating in a flexural mode, and said quartz crystal tuning forkresonator comprising: tuning fork tines each of which has a length, awidth and a thickness and the length greater than the width and thethickness; and a tuning fork base; said tuning fork tines and saidtuning fork base that are formed integrally; and electrodes disposedfacing each other on sides of said tuning fork tines so that theelectrodes disposed facing each other are of opposite electricalpolarity and said tuning fork tines are capable of vibrating in inversephase,

According to a second aspect of the present invention there is providedan electronic apparatus comprising a display portion and a quartzcrystal oscillator at least, and said electronic apparatus comprises atleast one quartz crystal oscillator comprising: an oscillating circuitcomprising; an amplification circuit comprising an amplifier at least,and a feedback circuit comprising a length-extensional mode quartzcrystal resonator which is one of a contour mode quartz crystalresonator.

According to a third aspect of the present invention, there is provideda method for manufacturing an electronic apparatus comprising a displayportion and a quartz crystal oscillator at least, and said electronicapparatus comprising at least one quartz crystal oscillator, said atleast one oscillator comprising: a quartz crystal oscillating circuitcomprising; an amplification circuit comprising an amplifier at least,and a feedback circuit comprising a quartz crystal resonator andcapacitors at least, said quartz crystal resonator being a quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,said quartz crystal tuning fork resonator comprising the steps of:forming integrally tuning fork tines each of which has a length, a widthand a thickness and the length greater than the width and the thicknessand a tuning fork base; disposing electrodes facing each other on sidesof said tuning fork tines so that the electrodes disposed facing eachother are of opposite electrical polarity and said tuning fork tinesvibrate an in inverse phase; and adjusting resonance frequency of saidquartz crystal tuning fork resonator after mounting it at a mountingportion by conductive adhesives or solder so that a frequency deviationis within a range of −100 PPM to +100 PPM.

According to a fourth aspect of the present invention, there areprovided a quartz crystal resonator, a quartz crystal unit and a quartzcrystal oscillator, each of which has a piezoelectric constant e₁₂ thatis within a range of 0.095 C/m² to 0.19 C/m².

Preferably, said tuning fork resonator is constructed so that figure ofmerit M₁ of a fundamental mode vibration is larger than figure of meritM₂ of a second overtone mode vibration.

Preferably, the quartz crystal oscillator with said tuning forkresonator is constructed so that a ratio of an amplification rate α₁ ofthe fundamental mode vibration and an amplification rate α₂ of thesecond overtone mode vibration of said amplification circuit is largerthan that of a feedback rate β₂ of the second overtone mode vibrationand a feedback rate β₁ of the fundamental mode vibration of saidfeedback circuit, and a product of the amplification rate α₁ and thefeedback rate β₁ of the fundamental mode vibration is larger than 1.

Preferably, the quartz crystal oscillator with said tuning forkresonator is constructed so that a ratio of an absolute value ofnegative resistance, |−RL₁| of the fundamental mode vibration of saidamplification circuit and series resistance R₁ of the fundamental modevibration is larger than that of an absolute value of negativeresistance, |−RL₂| of the second overtone mode vibration of saidamplification circuit and series resistance R₂ of the second overtonemode vibration.

Preferably, the length-extensional mode quartz crystal resonatorcomprises a vibrational portion, connecting portions and supportingportions, which are formed integrally by a particle method.

The present invention will be more fully understood by referring to thefollowing detailed specification and claims taken in connection with theappended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus;

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention;

FIG. 3 shows a diagram of the feedback circuit of FIG. 2;

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the first embodiment of thepresent invention;

FIG. 5 shows a A-A′ cross-sectional view of the tuning fork base of FIG.4, and illustrating electrode construction;

FIG. 6 shows a plan view of a quartz crystal tuning fork resonator ofFIG. 4;

FIG. 7 shows a plan view of a flexural mode, quartz crystal tuning forkresonator constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the second embodiment of the present invention;

FIG. 8 a and FIG. 8 b show a top view and a side view of alength-extensional mode quartz crystal resonator constructing a quartzcrystal oscillator, which constructs an electronic apparatus of thethird embodiment of the present invention;

FIG. 9 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the fourth embodiment of the present invention;

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fifth embodiment of thepresent invention;

FIG. 11 shows a step diagram of a method for manufacturing a quartzcrystal unit constructing a quartz crystal oscillator, which constructsan electronic apparatus of the present invention;

FIG. 12 is a general view of the conventional flexural mode, quartzcrystal tuning fork resonator constructing a quartz crystal oscillatorof the prior art, which constructs the conventional electronicapparatus;

FIG. 13 is a cross-sectional view of the tuning fork tines of FIG. 12,and illustrating electrode construction;

FIG. 14 shows a B-B′ cross-sectional view of the tuning fork tines ofFIG. 4;

FIG. 15 shows a plan view of a quartz crystal unit of the presentinvention and omitting a lid, and constructing a quartz crystaloscillator and an electronic apparatus of the present invention;

FIG. 16 shows a plan view of a quartz crystal unit of the presentinvention and omitting a lid, and constructing a quartz crystaloscillator and an electronic apparatus of the present invention;

FIG. 17 shows a plan view of a quartz crystal unit of the presentinvention and omitting a lid, and constructing a quartz crystaloscillator and an electronic apparatus of the present invention;

FIG. 18 shows a relationship between a dimensional ratio R=W₀/L₀ and acut angle θ_(x) of a length extensional mode quartz crystal resonator togive a zero temperature coefficient;

FIG. 19 shows a top view (a) and a C-C′ cross-sectional view (b) of avibrational portion of a thickness shear mode quartz crystal resonatorconstructing a quartz crystal unit, and which constructs an electronicapparatus of the present invention.

FIG. 20 shows a plan view of a flexural mode, quartz crystal tuning forkresonator of the present invention, and constructing a quartz crystalunit, a quartz crystal oscillator and an electronic apparatus of thepresent invention;

FIG. 21 shows a D₁-D₂ cross-sectional view of the tuning fork tines ofFIG. 20;

FIG. 22 shows a D₃-D₄ cross-sectional view of the tuning fork tines ofFIG. 20;

FIG. 23 shows a plan view of a flexural mode, quartz crystal tuning forkresonator of the present invention, and constructing a quartz crystalunit, a quartz crystal oscillator and an electronic apparatus of thepresent invention;

FIG. 24 shows a J₁-J₂ cross-sectional view of the tuning fork tines ofFIG. 23; and

FIG. 25 shows a J₃-J₄ cross-sectional view of the tuning fork tines ofFIG. 23.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, the embodiments of the present inventionwill be described in more detail.

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus. As is shown in FIG. 1, the apparatus generally comprises amodem, a phonetic circuit, a timepiece circuit, a printing portion, ataking portion, an operation portion and a display portion. In thisprinciple, perception and scanning of reflection light of lightprojected on manuscript in the taking portion are performed by CCD(Charge Coupled Device), in addition, light and shade of the reflectionlight are transformed into a digital signal, and the signal is modulatedby the modem and is sent to a phone line (Communication line). Also, ina receiving side, a received signal is demodulated by the modem and isprinted on a paper in the print portion by synchronizing the receivedsignal with a signal of a sending side.

As shown in FIG. 1, a quartz crystal resonator which is one ofpiezoelectric resonators made of piezoelectric materials is used as aCPU clock of the control portion and the printing portion, as a clock ofthe phonetic circuit and the modem, and as a time standard of thetimepiece. Namely, the resonator constructs a quartz crystal oscillatorand an output signal of the oscillator is used. For example, it is usedas a signal to display time at the display portion. In this case, aquartz crystal tuning fork resonator, capable of vibrating in a flexuralmode is used, and e.g. as the CPU clock, a contour mode quartz crystalresonator such as a length-extensional mode quartz crystal resonator ora thickness shear mode quartz crystal resonator is used. In order to getthe facsimile apparatus of this embodiment which operates normally, anaccuracy output signal of the oscillator is required for the facsimileapparatus, which is one of the electronic apparatus of the presentinvention. Also, a digital display and an analogue display are includedin the display of the present invention. In this embodiment, two quartzcrystal resonators each of which vibrates in a different mode are usedin the electronic apparatus of the present invention. But, the presentinvention is not limited to this, two quartz crystal resonators each ofwhich vibrates in the same mode may be used in the electronic apparatusof the present invention. Namely, one of the two quartz crystalresonators is used as a signal for use in operation of the electronicapparatus to display time information at the display portion of theelectronic apparatus. One of the two quartz crystal resonators which isused as a signal for use in operation of the electronic apparatus todisplay time information at the display portion has a frequency ofoscillation of a fundamental mode of vibration. In more detail, apiezoelectric resonator has a fundamental mode of vibration and anovertone mode of vibration. It is needless to say that the fundamentalmode of vibration and the overtone mode of vibration thereof are definedas the same mode of vibration. For example, a thickness shear modequartz crystal resonator has a fundamental mode of vibration and a thirdovertone mode of vibration, the fundamental mode of vibration of thethickness shear mode quartz crystal resonator is, therefore, the samemode of vibration as the third overtone mode of vibration thereof. Instead of the quartz crystal, such a piezoelectric material may be usedas LiTaO₃, LiNbO₃, GaPO₄, and so on.

In this embodiment, though the facsimile apparatus is shown as anexample of an electronic apparatus, the present invention is not limitedto this, namely, the present invention includes all electronicapparatus, each of which comprises a quartz crystal oscillator and adisplay portion at least, for example, cellar phones, telephones, a TVset, cameras, a video set, video cameras, pagers, personal computers,printers, CD players, MD players, electronic musical instruments, carnavigators, car electronics, timepieces, IC cards and so forth.

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention. The quartz crystaloscillating circuit 1 comprises an amplifier (CMOS Inverter) 2, afeedback resistor 4, a drain resistor 7, capacitors 5, 6 and a flexuralmode, quartz crystal tuning fork resonator 3. Namely, the oscillatingcircuit 1 comprises an amplification circuit 8 having the amplifier 2and the feedback resistor 4, and a feedback circuit 9 having the drainresistor 7, the capacitors 5, 6 and the quartz crystal tuning forkresonator 3. In addition, an output signal of the oscillating circuit 1comprising the quartz crystal tuning fork resonator 3, capable ofvibrating in a fundamental mode, is outputted through a buffer circuit(not shown in FIG. 2).

In detail, an oscillation frequency of the fundamental mode vibration isoutputted through a buffer circuit as an output signal. According to thepresent invention, a nominal frequency of the fundamental mode vibrationof the resonator is within a range of 10 kHz to 200 kHz. Especially,32.768 kHz is an important frequency. In general, the output signal hasan oscillation frequency which is within a range of −100 PPM to +100 PPMto the nominal frequency, e.g. 32.768 kHz. In more detail, the quartzcrystal oscillator in this embodiment comprises a quartz crystaloscillating circuit and a buffer circuit, namely, the quartz crystaloscillating circuit comprises an amplification circuit and a feedbackcircuit, and the amplification circuit comprises an amplifier and afeedback resistor, and the feedback circuit comprises a flexural mode,quartz crystal tuning fork resonator, a drain resistor and capacitors.Also, flexural mode, quartz crystal tuning fork resonators which areused in a quartz crystal oscillator will be described in FIG. 4-FIG. 7in detail. Instead of the flexural mode, quartz crystal tuning forkresonator, a contour mode resonator such as a length-extensional modequartz crystal resonator, a width-extensional mode quartz crystalresonator and a Lame mode quartz crystal resonator or a thickness shearmode quartz crystal resonator may be used.

FIG. 3 shows a diagram of the feedback circuit of FIG. 2. Now, whenangular frequency ω_(i) of the flexural mode, quartz crystal tuning forkresonator 3, capable of vibrating in a flexural mode, a resistance R_(d)of the drain resistor 7, capacitance C_(g), C_(d) of the capacitors 5,6, crystal impedance R_(ei) of the quartz crystal resonator 3, an inputvoltage V₁, and an output voltage V₂ are taken, a feedback rate β_(i) isdefined by β_(i)=|V₂|_(i)/|V₁|_(i), where i shows vibration order, forexample, when i=1 and 2, they are for a fundamental mode vibration and asecond overtone mode vibration.

In addition, load capacitance C_(L) is given byC_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) andRd>>R_(ei), the feedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²),where k is expressed by a function of ω_(i), R_(d) and R_(ei). Also,R_(ei) is approximately equal to series resistance R₁.

Thus, it is easily understood from a relationship of the feedback rateβ_(i) and load capacitance C_(L) that the feedback rate of resonancefrequency for a fundamental mode vibration and an overtone modevibration becomes large, respectively, according to decrease of loadcapacitance C_(L). Therefore, when C_(L) has a small value, anoscillation of the overtone mode occurs very easily, instead of that ofthe fundamental mode. This is the reason why a maximum amplitude of theovertone mode vibration becomes smaller than that of the fundamentalmode vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

As it is also one object of the present invention to provide a quartzcrystal oscillator having a flexural mode, quartz crystal tuning forkresonator, capable of vibrating in a fundamental mode and having a highfrequency stability (high time accuracy) of an output signal, and havingreduced electric current consumption, in this embodiment, loadcapacitance C_(L) is less than 25 pF to reduce electric currentconsumption. To get much reduced electric current consumption, C_(L) ispreferably less than 15 pF because electric current consumption isproportional to C_(L).

In addition, in order to suppress a second overtone mode vibration andto obtain a quartz crystal oscillator having an output signal of anoscillation frequency of a fundamental mode vibration, the quartzcrystal oscillator in this embodiment is constructed so that itsatisfies a relationship of α₁/α₂>β₂/β₁ and α₁β₁>1, where α₁ and α₂ are,respectively, an amplification rate of the fundamental mode vibrationand the second overtone mode vibration of an amplification circuit, andβ₁ and β₂ are, respectively, a feedback rate of the fundamental modevibration and the second overtone mode vibration of a feedback circuit.

In other words, the quartz crystal oscillator is constructed so that aratio of the amplification rate α₁ of the fundamental mode vibration andthe amplification rate α₂ of the second overtone mode vibration of theamplification circuit is larger than that of the feedback rate β₂ of thesecond overtone mode vibration and the feedback rate β₁ of thefundamental mode vibration of the feedback circuit, and also a productof the amplification rate α₁ and the feedback rate β₁ of the fundamentalmode vibration is larger than 1. A description of the high frequencystability will be performed later.

Also, characteristics of the amplifier of the amplification circuitconstructing the quartz crystal oscillating circuit of this embodimentcan be expressed by negative resistance −RL_(i). For example, when i=1,negative resistance −RL₁ is for a fundamental mode vibration and wheni=2, negative resistance −RL₂ is for a second overtone mode vibration.In this embodiment, the quartz crystal oscillating circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of the fundamental mode vibration of the amplification circuitand series resistance R₁ of the fundamental mode vibration is largerthan that of an absolute value of negative resistance, |−RL₂| of thesecond overtone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration. That is to say, theoscillating circuit is constructed so that it satisfies a relationshipof |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit likethis, an oscillation of the second overtone mode can be suppressed, as aresult of which an output signal of a frequency of the fundamental modevibration can be provided because an oscillation of the fundamental modegenerates easily in the oscillating circuit.

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator 10 which is one of a contour mode resonator, constructinga quartz crystal oscillator, which constructs an electronic apparatus ofthe first embodiment of the present invention and its coordinate systemo-xyz. A cut angle θ which has a typical value of 0° to 10° is rotatedfrom a Z-plate perpendicular to the z axis about the x axis. Namely, theflexural mode, quartz crystal tuning fork resonator has the cut angel ofZYw(0° to 10°) according to an expression of the IEEE notation. Theresonator 10 comprises two tuning fork tines (vibrating tines) 20 and 26and a tuning fork base (a base) 40. The tines 20 and 26 have grooves 21and 27 respectively, with the grooves 21 and 27 extending into the base40. Also, the base 40 has the additional grooves 32 and 36. In addition,the tines 20 and 26 vibrate in a flexural mode of a fundamental mode andan inverse phase.

FIG. 5 shows an A-A′ cross-sectional view of the tuning fork base 40 ofthe quartz crystal resonator 10 in FIG. 4. In FIG. 5, the shape of theelectrode construction within the base 40 for the quartz crystalresonator of FIG. 4 is described in detail. The section of the base 40which couples to the tine 20 has the grooves 21 and 22 cut into theobverse and reverse faces of the base 40. Also, the section of the base40 which couples to the tine 26 has the grooves 27 and 28 cut into theobverse and reverse faces of the base 40. In addition to these grooves,the base 40 has the grooves 32 and 36 cut between the grooves 21 and 27,and also, the base 40 has the grooves 33 and 37 cut between the grooves22 and 28.

Furthermore, the grooves 21 and 22 have the first electrodes 23 and 24both of the same electrical polarity, the grooves 32 and 33 have thesecond electrodes 34 and 35 both of the same electrical polarity, thegrooves 36 and 37 have the third electrodes 38 and 39 both of the sameelectrical polarity, the grooves 27 and 28 have the fourth electrodes 29and 30 both of same electrical polarity and the sides of the base 40have the fifth and sixth electrodes 25 and 31, each of oppositeelectrical polarity. In more detail, the fifth, fourth, and secondelectrodes 25, 29, 30, 34 and 35 have the same electrical polarity,while the first, sixth and third electrodes 23, 24, 31, 38 and 39 havethe opposite electrical polarity to the others. Two electrode terminalsE and E′ are constructed. That is, the electrodes disposed inside thegrooves constructed opposite each other in the thickness (z axis)direction have the same electrical polarity. Also, the electrodesdisposed opposite each other across adjoining grooves have oppositeelectrical polarity.

In addition, the resonator has a thickness t of the tines or the tinesand the base, and a groove thickness t₁. It is needless to say that theelectrodes are disposed inside the grooves and on the sides of thetines. In this embodiment, the first electrodes 23 and 24 are disposedat the tine and the base, and also, the fourth electrodes 29 and 30 aredisposed at the tine and the base. In addition, the electrodes aredisposed on the sides of the tines opposite each other to the electrodesdisposed inside the grooves. Namely, the electrodes are disposedopposite each other inside the grooves and on the sides of the tines sothat the electrodes disposed opposite each other are of oppositeelectrical polarity. Additionally, electrodes are disposed facing eachother on the sides of the tines so that the electrodes disposed facingeach other are of opposite electrical polarity, and the tines arecapable of vibrating in inverse phase. In more detail, a first tuningfork tine and a second tuning fork tine, and a tuning fork base areformed integrally, an electrode is disposed on both sides of the firsttine and the second tine so that the electrodes disposed (facing eachother) on inner sides of the first and second tines are of oppositeelectrical polarity. Therefore, the disposition of the electrodesdisposed inside the grooves and on the sides of the tuning fork tines,described above is the same as that of the electrodes shown in FIG. 14which shows a B-B′ cross-sectional view of the tuning fork tines 20, 26of the quartz crystal resonator 10 in FIG. 4, namely, the electrodes 23,24 are connected to the electrodes 31, 43 to define an electrodeterminal F, while the electrodes 29, 30 are connected to the electrodes25, 44 to define an electrode terminal F′. It is needless to say thatthe electrode terminal F is electrically connected to the electrodeterminal E and the electrode terminal F′ is electrically connected tothe electrode terminal E′.

When a direct current voltage is applied between the electrode terminalsE and E′ (E terminal: plus, E′ terminal: minus), an electric field E_(x)occurs in the arrow direction as shown in FIG. 5. As the electric fieldE_(x) occurs perpendicular to the electrodes disposed on the base, theelectric field E_(x) has a very large value and a large distortionoccurs at the base, so that the quartz crystal tuning fork resonator isobtained with a small series resistance R₁ and a high quality factor Q₁,even if it is miniaturized.

FIG. 6 shows a plan view of the resonator 10 of FIG. 4. In FIG. 6, theconstruction and the dimension of grooves 21, 27, 32 and 36 aredescribed in detail. The groove 21 is constructed to include a portionof the central line 41 of the tine 20, and the groove 27 is similarlyconstructed to include a portion of the central line 42 of the tine 26.The width W₂ of the grooves 21 and 27 (groove width W₂) which include aportion of the central lines 41 and 42 respectively, is preferablebecause moment of inertia of the tines 20 and 26 becomes large and thetines can vibrate in a flexural mode easily. As a result, the quartzcrystal tuning fork resonator capable of vibrating in a fundamental modecan be obtained with a small series resistance R₁ and a high qualityfactor Q₁.

In more detail, when part widths W₁, W₃ and a groove width W₂ are taken,the tine width W of the tines 20 and 26 has a relationship ofW=W₁+W₂+W₃, and the part widths W₁, W₃ are constructed so that W₁≧W₃ orW₁<W₃. In addition, the groove width W₂ is constructed so that W₂≧W₁,W₃. In this embodiment, also, the grooves are constructed at the tinesso that a ratio (W₂/W) of the groove width W₂ and the tine width W islarger than 0.35 and less than 1, preferably larger than 0.35 and lessthan 0.85, and a ratio (t₁/t) of the groove thickness t₁ and thethickness t of the tines (tine thickness t) is less than 0.79, to obtainvery large moment of inertia of the tines. That is, the flexural mode,quartz crystal tuning fork resonator, capable of vibrating in thefundamental mode, and having a good frequency stability can be providedwith a small series resistance R₁, a high quality factor Q₁ and a smallcapacitance ratio r₁ because electromechanical transformation efficiencyof the resonator becomes large markedly.

Likewise, a length l₁ of the grooves 21, 27 provided at the tines 20, 26extends into the base 40 in this embodiment (which has a dimension ofthe length l₂ and the length l₃ of the grooves). Therefore, a groovelength and a length of the tines are given by (l₁−l₃) and (l−l₂),respectively, and a ratio of (l₁−l₃) and (l−l₂) is within a range of 0.3to 0.8, preferably, 0.4 to 0.8 to get a flexural mode tuning forkresonator with series resistance R₁ of a fundamental mode vibrationsmaller than series resistance R₂ of a second overtone mode vibration.In other words, a groove length is within a range of 30% to 80%,preferably, 40% to 80% of a length of each of the tines, so that aflexural mode tuning fork resonator with a reduced series resistance R₁and a small motional inductance L₁ of a fundamental mode vibration andhaving shock proof can be obtained when the flexural mode tuning forkresonator is miniaturized. Also, a length l₂ of the base is less than0.5 mm, preferably, within a range of 0.29 mm to 0.48 mm or within arange of 0.12 mm to 0.255 mm or within a range of 0.264 mm to 0.277 mm,so that a miniaturized flexural mode tuning fork resonator can beobtained with reduced energy losses which are caused by vibration whenit is mounted on a mounting portion of a case. As be well known, theresonator can be expressed by an electrical equivalent circuitcomprising motional capacitance C₁, motional inductance L₁, seriesresistance R₁ connected in series, and shunt capacitance C₀ connected toC₁, L₁ and R₁ in parallel.

Furthermore, the total length l is determined by the frequencyrequirement and the size of the housing case. Simultaneously, to get aflexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode with suppression of the second overtonemode vibration which is an unwanted mode vibration, there is a closerelationship between the groove length l₁ and the total length l.Namely, a ratio (l₁/l) of the groove length l₁ and the total length l iswithin a range of 0.2 to 0.78 because the quantity of charges whichgenerate within the grooves and on the sides of the tines or the tinesand the base can be controlled by the ratio, as a result, the secondovertone mode vibration which is an unwanted mode vibration, can besuppressed, and simultaneously, a frequency stability of the fundamentalmode vibration gets high. Therefore, the flexural mode, quartz crystaltuning fork resonator, capable of vibrating easily in a fundamental modeand having high frequency stability can be provided. Also, the totallength l is less than 2.18 mm, preferably, within a range of 1.2 mm to 2mm, more preferably, 0.8 mm to 1.2 mm, and groove length l₁ is less than1.29 mm, preferably, within a range of 0.32 mm to 1.1 mm, morepreferably, within a range of 0.32 mm to 0.85 mm, to get a smaller-sizedtuning fork resonator with about 32.768 kHz and a small motionalinductance L₁ which vibrates in a flexural mode and a fundamental mode.

In more detail, series resistance R₁ of the fundamental mode vibrationbecomes smaller than series resistance R₂ of the second overtone modevibration. Namely, R₁<R₂, preferably, R₁<0.86R₂, therefore, a quartzcrystal oscillator comprising an amplifier (CMOS inverter), capacitors,resistors and a quartz crystal unit with the quartz crystal tuning forkresonator of this embodiment can be obtained, which is capable ofvibrating in the fundamental mode easily. In addition, in thisembodiment the grooves 21 and 27 of the tines 20 and 26 extend into thebase 40 in series, but embodiment of the present invention includes aplurality of grooves divided into the length direction of the tines. Inaddition, the grooves may be constructed only at the tines (l₃=0).

In this embodiment, the groove length l₁ corresponds to electrode lengthdisposed inside the grooves, though the electrode is not shown in FIG.6, but, when the electrode length is less than the groove length, thelength l₁ is of the electrode length. Namely, the ratio (l₁/l) in thiscase is expressed by a ratio of electrode length l₁ of the grooves andthe total length l. In order to achieve the above-mentioned object, itmay be satisfied with at least one groove with the ratio constructed atthe obverse and reverse faces of each tine. As a result, the flexuralmode, quartz crystal tuning fork resonator, capable of vibrating veryeasily in the fundamental mode and having the high frequency stabilitycan be realized. Also, a fork portion of this embodiment has arectangular shape, but this invention is not limited to this, forexample, the fork portion may have a U shape.

In addition, a space of between the tines is given by W₄, and in thisembodiment, the space W₄ and the groove width W₂ are constructed so thatW₄≧W₂, and more, the space W₄ is within a range of 0.05 mm to 0.35 mmand the groove width W₂ is within a range of 0.03 mm to 0.12 mm becauseit is easy to form a tuning fork shape and grooves of the tuning forktines separately by a photo-lithographic process and an etching process,consequently, a frequency stability for a fundamental mode vibrationgets higher than that for a second overtone mode vibration. In thisembodiment, a quartz wafer with the thickness t of 0.05 mm to 0.15 mm isused. In order to get a smaller-sized quartz crystal tuning forkresonator, capable of vibrating in a flexural mode, and a small motionalinductance L₁, it is necessary that groove width W₂ is less than 0.07mm, preferably, larger than 0.015 mm and less than 0.04 mm and tinewidth W is less than 0.18 mm, and preferably, the W is larger than 0.05mm and less than 0.1 mm, more preferably, larger than 0.03 mm and lessthan 0.075 mm. Also, a groove thickness t₁ is within a range of 0.01 mmto 0.085 mm approximately, and part widths W₁, W₃ are less than 0.021mm, preferably, less than 0.015 mm. In more detail, a dimension of thepart widths W₁, W₃ is very dependent on a manufacturing technology.Therefore, when the technology is taken into account, W₁ and W₃ have avalue of larger than 0.008 mm and less than 0.015 mm, preferably, largerthan 0.01 mm and less than 0.014 mm to get a small motional inductanceL₁. In addition, the groove provided on at least one of the obverse faceand the reverse face of the tuning fork tines of the present inventionmay be a through hole, namely, the groove thickness t₁=0. Moreover,another example of the tuning fork tines having t₁=0 is shown in FIG. 20and which shows a plan view of a flexural mode, quartz crystal tuningfork resonator 600. In detail, the resonator 600 comprises tuning forktines 601, 602 and tuning fork base 603, the base 603 has cut portions604, 605, and the tines 601, 602 have central linear portions 616, 617,respectively. The tine 601 has through holes 606, 608, 610 and grooves607, 609 and the tine 602 has through holes 611, 613, 615 and grooves612, 614. Each of the tines 601, 602 has a width W, and the throughholes and the grooves have a width W₂ larger than or equal to partwidths W₁, W₃, where W is given by W=W₁+W₂+W₃. Namely, the tuning forktines have a first tuning fork tine 601 and a second tuning fork tine602, and three through holes are formed at each of the first and secondtuning fork tines so that a width W₂ of the through holes is greaterthan the part widths W₁ and/or W₃. For example, the width W₂ of thethrough holes has a value lager than 0.02 mm and less than 0.04 mm andthe part widths W₁ and W₃ have a value larger than 0.008 mm and lessthan 0.014 mm. In this embodiment, the through holes are dived into thelength direction of the first and second tuning fork tines. When thefirst tuning fork tine 601 has three through holes comprising first,second and third through holes 610, 608, 606 divided in the lengthdirection, the groove 609 is formed between the first through 610 andsecond through hole 608 and the groove 606 is formed between the secondthrough hole 608 and the third through hole 606. Similar to this, whenthe second tuning fork tine 602 has three through holes comprisingfirst, second and third through holes 615, 613, 611 divided in thelength direction, the groove 614 is formed between the first through 615and second through hole 613 and the groove 612 is formed between thesecond through hole 613 and the third through hole 611. In other words,each of the first and second tuning fork tines has three through holesdivided in the length direction and a groove is formed in at least oneor each of the obverse and reverse faces between two through holes. Inthis embodiment, though a groove is formed between two through holes,but this invention is not limited to this, the groove may be not formedbetween the two through holes. Namely, a frame portion is formed betweenthe two through holes. In addition, FIG. 21 shows a D₁-D₂cross-sectional view of the tuning fork tines 601, 602. The tine 601 haselectrodes 618, 621 disposed on side surfaces and electrodes 619, 620disposed in grooves 609, 626, while the tine 602 has electrodes 622, 625disposed on side surfaces and electrodes 623, 624 disposed in grooves614, 627. The electrodes 618, 621, 623, 624 are connected electricallyto form an electrode terminal G₁, while the electrodes 619, 620, 622,625 are connected electrically to form an electrode terminal G₂.Moreover, FIG. 22 shows a D₃-D₄ cross-sectional view of the tuning forktines 601, 602. The tine 601 has electrodes 618, 621 disposed on sidesurfaces and electrodes 628, 629 disposed in a through hole 610, whilethe tine 602 has electrodes 622, 625 disposed on side surfaces andelectrodes 630, 631 disposed in a through hole 615. The electrodes 618,621, 630, 631 are connected electrically to form an electrode terminalG₃, while the electrodes 628, 629, 622, 625 are connected electricallyto form an electrode terminal G₄. The electrode terminals G₁ and G₃ havethe same electrical polarity, while the electrode terminals G₂ and G₄have the same electrical polarity different from the electrical polarityof the electrode terminals G₁ and G₃. When an alternating currentvoltage is applied to the electrode terminals G₁, G₃ and the electrodeterminals G₂, G₄, the tuning fork resonator vibrates in a flexural modeof an inverse phase. In this embodiment, frame portions are not shown atthe tuning fork base 603, but the tuning fork base may have frameportions protruding from the tuning fork base. Moreover, when a lengthof the grooves and a length of the through holes are defined by l_(m)and l_(a), respectively, there are two relationships so that l_(m)≧l_(a)or l_(m)<l_(a). In more detail, a length l_(a) of the through holes inthis embodiment is within a range of 0.03 mm to 0.45 mm, preferably,0.05 mm to 0.3 mm and a length l_(m) of the grooves is within a range of0.01 mm to 0.5 mm, preferably, 0.025 mm to 0.35 mm. One of the tworelationships is selected so that the tuning fork resonator has a smallmotional inductance L₁. It is needless to say that a relationship of thelength l_(a) and the length l_(m) can be applied to a tuning forkresonator in FIG. 23. In addition, a further example of the tuning forktines having t₁=0 is shown in FIG. 23 and which shows a plan view of aflexural mode, quartz crystal tuning fork resonator 650. In detail, theresonator 650 comprises tuning fork tines 651, 652 and tuning fork base653, the base 653 has cut portions 654, 655, and the tines 651, 652 havecentral linear portions 666, 667, respectively. The tine 651 has throughholes 656, 657, 658, 659 and a groove 660 and the tine 652 has throughholes 661, 662, 663, 664 and a groove 665. Each of the tines 601, 602has a width W, and the grooves have a width W₂ larger than or equal topart widths W₁, W₃, where W is given by W=W₁+W₂+W₃. Namely, when each ofthe first and second tuning fork tines has a first side surface and asecond side surface opposite the first side surface, and obverse andreverse faces each of which has a central linear portion, a through holeis formed between the first side surface and the central linear portionand/or a through hole is formed between the second side surface and thecentral linear portion so that the central linear portion is notincluded in the through hole. Namely, a width of the through hole isless than a half of the tine width W. In this embodiment, the throughholes are divided into the width and length directions of thecorresponding one of the first and second tuning fork tines. The groove660 is formed between the through holes 656, 657, between the throughholes 658, 659, between 656, 658 and between the through holes 657, 659,while the groove 665 is formed between the through holes 661, 662,between the through holes 663, 664, between 661, 663 and between thethrough holes 662, 664. Namely, the through holes 656, 657, 658, 659 areformed in the groove 660 and the through holes 661, 662, 663, 664 areformed in the groove 665. In this embodiment, though a groove is formedbetween the through holes, this invention is not limited to this, butthe groove may be not formed between the through holes. In addition, twothrough holes at each of left and right sides of the central linearportion are formed in the length direction in this embodiment, but thethrough holes more than two may be formed in the length direction. Inaddition, two through holes are formed symmetrically in the widthdirection to the central linear portion in this embodiment, but the twothrough holes may be formed asymmetrically in the width direction to thecentral linear portion. Moreover, FIG. 24 shows a J₁-J₂ cross-sectionalview of the tuning fork tines 651, 652. The tine 651 has electrodes 668,672 disposed on side surfaces and electrodes 669, 670, 671 disposed inthrough holes 656, 657, while the tine 652 has electrodes 673, 678disposed on side surfaces and electrodes 674, 675, 676 disposed inthrough hole 661, 662. The electrodes 668, 672, 674, 675, 676 areconnected electrically to form an electrode terminal N₁, while theelectrodes 669, 670, 671, 673, 678 are connected electrically to form anelectrode terminal N₂. In addition, FIG. 25 shows a J₃-J₄cross-sectional view of the tuning fork tines 651, 652. The tine 651 haselectrodes 668, 672 disposed on side surfaces and electrodes 679, 680disposed in grooves 660, 683, while the tine 652 has electrodes 673, 678disposed on side surfaces and electrodes 681, 682 disposed in grooves665, 684. The electrodes 668, 672, 681, 682 are connected electricallyto form an electrode terminal N₃, while the electrodes 679, 680, 673,678 are connected electrically to form an electrode terminal N₄. Theelectrode terminals N₁ and N₃ have the same electrical polarity, whilethe electrode terminals N₂ and N₄ have the same electrical polaritydifferent from the electrical polarity of the electrode terminals N₁ andN₃. When an alternating current voltage is applied to the electrodeterminals N₁, N₃ and the electrode terminals N₂, N₄, the tuning forkresonator vibrates in a flexural mode of an inverse phase. In thisembodiment, frame portions are not shown at the tuning fork base 653,but the tuning fork base may have frame portions protruding from thetuning fork base. Moreover, the through holes are formed at each offirst and second tuning fork tines by etching simultaneously with thefirst and second tuning fork tines. But, at least one through hole maybe formed at each of first and second tuning fork tines by etching in astep different from the step of forming the first and second tuning forktines. In addition, each of the first and second tuning fork tines has aplurality of through holes in the length direction, an overall length ofthe through holes is within a range of 20% to 80%, preferably, 30% to70%, of a length of each of the tuning fork tines. Moreover, when awidth of the groove formed in the width direction between two throughholes and a width of the through holes are defined by w_(m) and w_(a),respectively, the groove and the through holes are formed so thatw_(m)≧w_(a) or w_(m)<w_(a). Namely, they are formed so that the tuningfork resonator has a small motional inductance L₁. Also, a width of thethrough holes in this embodiment is within a range of 0.008 mm to 0.03mm, preferably, 0.01 mm to 0.02 mm. As a result, the tuning forkresonator can be obtained with a small motional inductance L₁, so thatan oscillating circuit with the tuning fork resonator can be providedwith short rise-time of an output signal when an alternating currentvoltage is applied to the oscillating circuit.

In more detail, to obtain a flexural mode, quartz crystal tuning forkresonator with a high frequency stability which gives high timeaccuracy, it is necessary to obtain the resonator whose resonancefrequency is not influenced by shunt capacitance because quartz crystalis a piezoelectric material and the frequency stability is verydependent on the shunt capacitance. In order to decrease the influenceon the resonance frequency by the shunt capacitance, figure of meritM_(i) (hereafter a merit value M_(i)) plays an important role. Namely,the merit value M_(i) that expresses inductive characteristics,electromechanical transformation efficiency and a quality factor of aflexural mode, quartz crystal tuning fork resonator, is defined by aratio (Q_(i)/r_(i)) of a quality factor Q_(i) and capacitance ratior_(i), namely, M_(i) is given by M_(i)=Q_(i)/r_(i), where i showsvibration order of the resonator, and for example, when i=1 and 2, themerit values M₁ and M₂ are a value for a fundamental mode vibration anda second overtone mode vibration of the flexural mode, quartz crystaltuning fork resonator, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the merit value M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the frequency stability of the flexuralmode, quartz crystal tuning fork resonator becomes because the resonancefrequency f_(r) of the resonator is almost never dependent on the shuntcapacitance. Namely, the quartz crystal tuning fork resonator can beprovided with a high time accuracy.

In detail, the flexural mode, quartz crystal tuning fork resonator canbe obtained with the merit value M₁ of the fundamental mode vibrationlarger than the merit value M₂ of the second overtone mode vibration bythe above-described tuning fork shape, grooves and dimensions. That isto say, a relationship of M₁>M₂ is obtained. As an example, whenresonance frequency of a flexural mode, quartz crystal tuning forkresonator is about 32.768 kHz for a fundamental mode vibration and theresonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though thereis a distribution in production, the resonator has a value of M₁>65 andM₂<30, respectively.

Namely, the flexural mode, quartz crystal tuning fork resonator whichvibrates in the fundamental mode can be provided with high inductivecharacteristics, good electromechanical transformation efficiency (smallcapacitance ratio r₁ and small series resistance R₁) and a high qualityfactor. As a result, a frequency stability of the fundamental modevibration becomes higher than that of the second overtone modevibration, and simultaneously, the second overtone mode vibration can besuppressed because capacitance ratio r₂ and series resistance R₂ of thesecond overtone mode vibration become larger than capacitance ratio r₁and series resistance R₁ of the fundamental mode vibration,respectively. In particular, r₂ has a value larger than 1500 in thisembodiment.

Therefore, the resonator capable of vibrating in the fundamental modevibration can be provided with a high time accuracy because it has thehigh frequency stability. Consequently, a quartz crystal oscillatorcomprising the flexural mode, quartz crystal tuning fork resonator ofthis embodiment outputs an oscillation frequency of the fundamental modevibration as an output signal, and the frequency of the output signalhas a very high stability, namely, excellent time accuracy. In otherwords, the quartz crystal oscillator of this embodiment has a remarkableeffect such that a frequency change by ageing becomes extremely small.Also, an oscillation frequency of the resonator of this embodiment isadjusted so that a frequency deviation is within a range of −100 PPM to+100 PPM to a nominal frequency, e.g. 32.768 kHz, after mounting it at amounting portion of a case or a lid by conductive adhesives or solder.

In addition, the groove thickness t₁ of the present invention is thethinnest thickness of the grooves because quartz crystal is ananisotropic material and the groove thickness t₁ has a distribution whenit is formed by a chemical etching method. In detail, a groove shape ofthe sectional view of tuning fork tines in FIG. 5 has a rectangularshape, but the groove shape has an about U shape actually. In theabove-described embodiments, though the grooves are constructed at thetines, this invention is not limited to this, namely, a relationship ofthe merit values M₁ and M₂ can be applied to the conventional flexuralmode, quartz crystal tuning fork resonator and a relationship of aquartz crystal oscillating circuit comprising an amplification circuitand a feedback circuit can be also applied to the conventional flexuralmode, quartz crystal tuning fork resonator to suppress a second overtonemode vibration and to get a high frequency stability for a fundamentalmode vibration of the tuning fork resonator.

FIG. 7 shows a plan view of a flexural mode, quartz crystal tuning forkresonator 45 which is one of a contour mode quartz crystal resonator,constructing a quartz crystal oscillator, which constructs an electronicapparatus of the second embodiment of the present invention. Theresonator 45 comprises tuning fork tines 46, 47 and a tuning fork base48. The tines 46, 47 and the base 48 are formed integrally by a chemicaletching process. In this embodiment, the base 48 has cut portions 53 and54. Also, a groove 49 is constructed to include a portion of the centralline 51 of the tine 46, and a groove 50 is similarly constructed toinclude a portion of the central line 52 of the tine 47. In thisembodiment, the grooves 49 and 50 are constructed at a part of the tines46 and 47, and have groove width W₂ and groove length l₁. In moredetail, a groove area S (=W₂×l₁) has a value of 0.01 mm² to 0.12 mm²,preferably, greater than 0.01 mm² and less than 0.043 mm² because it isvery easy to form the grooves by a chemical etching process and thequartz crystal tuning fork resonator can be provided with goodelectromechanical transformation efficiency by the formation of thegrooves.

Namely, the quartz crystal tuning fork resonator, capable of vibratingin a fundamental mode and having a high frequency stability can beprovided with a small series resistance R₁ and a high quality factor Q₁.Therefore, a quartz crystal oscillator having the high frequencystability can be realized with an output signal of a frequency of thefundamental mode vibration. In this embodiment, though electrodes arenot shown in FIG. 7, the electrodes are disposed inside the grooves 49,50 and on sides of the tines 46 and 47, similar to the resonator of FIG.4. In detail, the electrodes are disposed opposite each other inside thegrooves and on the sides of the tines so that the electrodes disposedopposite each other are of opposite electrical polarity. In more detail,a groove is provided on both of an obverse face and a reverse face oftuning fork tines having a first tuning fork tine and a second tuningfork tine, and also, a first electrode is disposed inside the groove anda second electrode is disposed on both sides of the tuning fork tines.In addition, a quartz crystal tuning fork resonator has two electrodeterminals, the one of the electrode terminals comprises a firstelectrode disposed inside a groove provided on both of the obverse faceand the reverse face of the first tuning fork tine and a secondelectrode disposed on the both sides of the second tuning fork tine,such that the first and second electrodes are connected, and the otherof the electrode terminals comprises a second electrode disposed on theboth sides of the first tuning fork tine and a first electrode disposedinside a groove provided on both of the obverse face and the reverseface of the second tuning fork tine, such that the second and firstelectrodes are connected. In this embodiment, a groove is provided onboth of an obverse face and a reverse face of tuning fork tines, but thepresent invention in not limited to this, for example, a groove may beprovided on at least one of an obverse face and a reverse face of tuningfork tines.

In addition, the base 48 has cut portions 53 and 54, and the cut base 48has a dimension of width W₅ (tines side) and width W₆ (opposite side tothe tines side). Also, the cut base 48 has a length l₄ between one ofthe cut portions and the side opposite to the tines side, and the lengthl₄ is within a range of 0.05 mm to 0.3 mm, preferably, 0.12 mm to 0.25mm to reduce energy losses which are caused by vibration. When the base48 is mounted at a mounting portion (e.g. on two lead wires for apackage of a tubular type) of a case or a lid of a surface mounting typeor a tubular type by solder or conductive adhesives, it is necessary tosatisfy W₆≧W₅ to decrease energy losses by vibration. The cut portions53 and 54 are very effective to decrease the energy losses. Therefore,the flexural mode, quartz crystal tuning fork resonator, capable ofvibrating in the fundamental mode and having the high frequencystability (high time accuracy) can be provided with a small seriesresistance R₁ and a high quality factor Q₁. Also, the width dimensionsW=W₁+W₂+W₃ and W₄, and the length dimensions l₁, l₂ and l are as alreadydescribed in relation to FIG. 6. In addition, a shape of the tuning forkbase according to the present invention is not limited to that of thisembodiment, for example, a tuning fork base may have a frame portionprotruding from the tuning fork base, and the frame portion is mountedat a mounting portion of a case or a lid of a package. The matterdescribed above implies that, for example, when the tuning fork tineshave a first tuning fork tine and a second tuning fork tine, the firsttuning fork tine is between the second tuning fork tine and the frameportion protruding from the tuning fork base as shown in FIG. 15 whichshows a plan view of a quartz crystal unit and omitting a lid. In moredetail, the quartz crystal unit 250 comprises a quartz crystal tuningfork resonator 255 capable of vibrating in a flexural mode of an inversephase, a case 256 for housing the resonator and a lid for covering anopen end of the case (not shown here). Namely, the resonator 255comprises tuning fork tines 257, 258 and a tuning fork base 259connected to the tuning fork tines, and the tuning fork base 259 has aframe portion 260 protruding from the tuning fork base. Also, the case256 has mounting portions 261 and 262, and the frame portion 260 ismounted on the mounting portion 261 of the case 256. In detail, anelectrode 267 disposed at the frame portion 260 is connected to anelectrode 268 disposed on the mounting portion 261 by adhesives 263 or ametal such as solder, and similarly, an electrode 269 disposed on thetuning fork base 259 is connected to an electrode 270 disposed on themounting portion 262 by adhesives 264 or a metal such as solder. Inaddition, the tuning fork tines 257, 258 have grooves 271, 273 (notshown here), 272 and 274 (not shown here), the grooves 271 and 272 areformed opposite to the grooves 273 and 274 in the thickness direction,respectively. The electrodes 271 a and 273 a disposed inside the grooves271 and 273 of the tine 257 are connected to the electrodes 275 and 276disposed on side surfaces of the tine 258 to define a first electrodeterminal, while the electrodes 272 a and 274 a disposed inside thegrooves 272 and 274 of the tine 258 are connected to the electrodes 277and 278 disposed on side surfaces of the tine 257 to define a secondelectrode terminal. Moreover, each of the tines 257, 258 has a width Wand a width W_(g) greater than the width W, preferably, the width W_(g)is less than three times of the width W to get a small motionalinductance L₁. As a result of which the tuning fork resonator can beprovided with a smaller size because the width W_(g) operates as massand a short length of the tuning fork tines can be obtained for afrequency of oscillation, e.g. 32.768 kHz. For example, when the width Wis larger than 0.03 mm and less than 0.075 mm, the width W_(g) is largerthan 0.04 mm and less than 0.23 mm. For example, a difference (W_(g)−W)is within a range of 0.008 mm to 0.1 mm, preferably, 0.01 mm to 0.05 mmto get enough mass effect. Also, each of the tines 257, 258 has a lengthl_(g) less than about 80% of a length of each of the tines measured fromthe free end of each of the tines. This is the reason why when each ofthe tines has the width W with a frequency, e.g. 32.8 kHz with thelength l_(g)=0, about the same frequency can be obtained as thefrequency of 32.8 kHz for the width W by forming the length l_(g) ofabout 80%. Namely, the tuning fork resonator can be obtained with asmall motional inductance L₁ because the width of the tines becomeslarger actually and the electromechanical transformation efficiency getslarger. In order to get a large mass effect by the length l_(g), each ofthe tines, preferably, has the length l_(g) less than a half of thelength of each of the tines measured from the free end of each of thetines. For example, the length l_(g) is larger than 0.15 mm and lessthan 1.1 mm, preferably, larger than 0.2 mm and less than 0.7 mm. Ingeneral, metal films for adjusting an oscillation frequency of theresonator are formed on main surfaces having the width W_(g), and theoscillation frequency is adjusted by trimming at least one of the metalfilms. In addition, the tuning fork base has cut portions 265, 266 andthe length l₄, and the frame portion is connected to the tuning forkbase having the length l₄. In addition, another example is shown in FIG.16 which shows a plan view of a quartz crystal unit and omitting a lid.In more detail, the quartz crystal unit 350 comprises a quartz crystaltuning fork resonator 355 capable of vibrating in a flexural mode of aninverse phase, a case 356 for housing the resonator and a lid forcovering an open end of the case (not shown here). Namely, the resonator355 comprises tuning fork tines 357, 358 and a tuning fork base 359connected to the tuning fork tines, and the tuning fork base 359 has twoframe portions 360 a, 360 b protruding from the tuning fork base. Also,the case 356 has mounting portions 361 and 362, and the frame portions360 a and 360 b is, respectively, mounted on the mounting portion 361and 362 of the case 356. In detail, an electrode 367 disposed at theframe portion 360 a is connected to an electrode 368 disposed on themounting portion 361 by adhesives 363 or a metal such as solder, andsimilarly, an electrode 369 disposed at the frame portion 360 b isconnected to an electrode 370 disposed on the mounting portion 362 byadhesives 364 or a metal such as solder. In addition, the tuning forkbase has two cut portions 365 and 366, the tuning fork tines 357, 358have the same as the grooves, the electrodes and the shape of the tuningfork tines shown in FIG. 15. In addition, a further example is shown inFIG. 17 which shows a plan view of a quartz crystal unit and omitting alid. In more detail, the quartz crystal unit 450 comprises a quartzcrystal tuning fork resonator 455 capable of vibrating in a flexuralmode of an inverse phase, a case 456 for housing the resonator and a lidfor covering an open end of the case (not shown here). Namely, theresonator 455 comprises tuning fork tines 457, 458 and a tuning forkbase 459 connected to the tuning fork tines, and the tuning fork base459 has a frame portion 460 protruding from the tuning fork base. Also,the case 456 has mounting portions 461, and the frame portion 460 ismounted on the mounting portion 461 of the case 456. In detail, anelectrode 467 disposed at the frame portion 460 is connected to anelectrode 468 disposed on the mounting portion 461 by adhesives 463 or ametal such as solder, and similarly, an electrode 469 disposed at theframe portion 460 is connected to an electrode 470 disposed on themounting portion 461 by adhesives 464 or a metal such as solder. Inaddition, the tuning fork tines 457, 458 have the same as the groovesand the electrodes shown in FIG. 14. Namely, the frame portionprotruding from the tuning fork base is between the first tuning forktine and the second tuning fork tine, and is mounted on the mountingportion of the case. In addition, when each of the first and secondtuning fork tines has a mass M_(t) and the frame portion has a massM_(f), a summation of (2M_(t)+M_(f)) is greater than a mass M_(b) of thetuning fork base having a length l₂ to get good shock-proof, preferably,a summation of (2M_(t)+M_(f)/2) is greater than a mass M_(b) of thetuning fork base to get further good shock-proof.

FIG. 8 a and FIG. 8 b are a top view and a side view for alength-extensional mode quartz crystal resonator which is one of acontour mode resonator, constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the third embodiment of thepresent invention. The resonator 62 comprises a vibrational portion 63,connecting portions 66, 69 and supporting portions 67, 80 includingrespective mounting portions 68, 81. In addition, the supportingportions 67 and 80 have respective holes 67 a and 80 a. Also, electrodes64 and 65 are disposed opposite each other on upper and lower faces ofthe vibrational portion 63, and the electrodes have opposite electricalpolarities. Namely, a pair of electrodes is disposed on the vibrationalportion. In this case, a fundamental mode vibration can be excitedeasily. In more detail of this embodiment, the resonator 62 has thevibrational portion 63, first and second supporting portions 67, 80, andfirst and second connecting portion 66, 69. Namely, the first supportingportion is connected to the vibrational portion through the firstconnecting portion, and the second supporting portion is connected tothe vibrational portion through the second connecting portion, so thattwo supporting portions are constructed. Therefore, the two supportingportions may have the first supporting portion and the second supportingportion connected each other, namely, it is needless to say that thesupporting portions of the present invention include the supportingportions connected each other.

In addition, the electrode 64 extends to the mounting portion 81 throughthe one connecting portion 69 and the electrode 65 extends to themounting portion 68 through the other connecting portion 66. In thisembodiment, the electrodes 64 and 65 disposed on the vibrational portion63 extend to the mounting portions of the different direction eachother. But, the electrodes may be constructed in the same direction. Theresonator in this embodiment is mounted on fixing portions of a case ora lid at the mounting portions 68 and 81 by conductive adhesives orsolder.

Here, a cutting angle of the length-extensional mode quartz crystalresonator is shown. First, a quartz crystal plate perpendicular to xaxis, so called, X plate quartz crystal is taken. Length L₀, width W₀and thickness T₀ which are each dimension of the X plate quartz crystalcorrespond to the respective directions of y, z and x axes.

Next, this X plate quartz crystal is, first, rotated with an angle θ_(x)of −30° to +30° about the x axis, and second, rotated with an angleθ_(y) of −40° to +40° about y′ axis which is the new axis of the y axis.In this case, the new axis of the x axis changes to x′ axis and the newaxis of the z axis changes to z″ axis because the z axis is rotatedtwice about two axes. The length-extensional mode quartz crystalresonator of the present invention is formed from the quartz crystalplate with the rotation angles.

In other words, according to an expression of IEEE notation, a cuttingangle of the resonator of the present invention can be expressed byXYtl(−30° to +30°)/(−40° to +40°). By choosing a cutting angle of theresonator, a turn over temperature point T_(p) can be taken at anarbitrary temperature. In this embodiment, length L₀, width W₀ andthickness T₀ correspond to y′, z″ and x′ axes, respectively. But, whenthe X plate is rotated once about the x axis, the z″ axis corresponds tothe z′ axis. In addition, the vibrational portion 63 has a dimension oflength L₀ greater than width W₀ and thickness T₀ smaller than the widthW₀. Namely, a coupling between length-extensional mode andwidth-extensional mode gets so small as it can be ignored, as a resultof which, the quartz crystal resonator can vibrate in a singlelength-extensional mode.

In more detail, resonance frequency of the length-extensional moderesonator is inversely proportional to length L₀, and it is almostindependent on such an other dimension as width W₀, thickness T₀,connecting portions and supporting portions. Also, in order to obtain alength-extensional mode quartz crystal resonator capable of vibrating ina fundamental mode with a frequency of 1 MHz to 10 MHz, the length L₀ iswithin a range of about 0.26 mm to about 2.7 mm. In addition, when alength-extensional mode resonator vibrates in an overtone mode, an oddnumber (n) pair of electrodes are disposed on a vibrational portion ofthe resonator, where n has a value of 1, 3, 5, . . . . In this case, thelength L₀ is within a range of about (0.26 to 2.7)×n mm. Thus, theminiature length-extensional mode resonator can be provided with thefrequency of 1 MHz to 10 MHz. In addition, FIG. 18 shows a relationshipbetween a dimensional ratio R=W₀/L₀ and a cut angle θ_(x) of thelength-extensional mode quartz crystal resonator to give a zerotemperature coefficient, namely, when the ratio R is in the range of0.325 to 0.475 and the cut angle θ_(x) is in the range of about 7° toabout 22°, there are many zero temperature coefficients, where the cutangle θ_(x) is defined by XYt(θ_(x)) according to an expression of theIEEE notation. In addition, when the ratio R is in the range of 0.3 to0.325 and 0.475 to 0.5, and the cut angle θ_(x) is in the range of 6° to7° and 22° to 23°, there is a small first order temperature coefficient.Therefore, in order to get a turn over temperature point over a widetemperature range, the ratio R is in the range of 0.3 to 0.5, the cutangle of the resonator is within a range of XYt(6° to 23°).

Next, a value of a piezoelectric constant e₁₂ (=e′₁₂) is described,which is of great importance and necessary to excite a flexural mode,quartz crystal resonator and a length-extensional mode quartz crystalresonator of the present invention. The larger a value of thepiezoelectric constant e₁₂ becomes, the higher electromechanicaltransformation efficiency becomes. The piezoelectric constant e₁₂ of thepresent invention can be calculated using the piezoelectric constantse₁₁=0.171 C/m² and e₁₄=−0.0406 C/m² of quartz crystal. As a result, thepiezoelectric constant e₁₂ of the present invention is within a range of0.095 C/m² to 0.19 C/m² approximately in an absolute value. It is,therefore, easily understood that this value is enough large to obtain aflexural mode, quartz crystal tuning fork resonator and alength-extensional mode quartz crystal resonator with a small seriesresistance R₁ and a high quality factor Q. Especially, in order toobtain a flexural mode, quartz crystal tuning fork resonator with asmaller series resistance R₁, the e₁₂ is within a range of 0.12 C/m² to0.19 C/m² in the absolute value, and also, a groove and electrodes areprovided on at least one of an obverse face and a reverse face of tuningfork tines so that when each tuning fork tine is divided into twoportions (an inner portion located at a fork side and an outer portionlocated opposite to the fork side) versus a central line portionthereof, a value of e₁₂ of each portion of each tuning fork tine has anopposite sign each other. Namely, when the one of the two portions hase₁₂ of a plus sign, the other of the two portions has e₁₂ of a minussign. In more detail, a groove and electrodes are provided at tuningfork tines so that a sign of e₁₂ of inner portions of each tuning forktine is opposite to the sign of e₁₂ of outer portions of each tuningfork tine.

When an alternating current voltage is applied between the electrodes 64and 65 shown in FIG. 8 b, an electric field E_(x) occurs alternately inthe thickness direction, as shown by the arrow direction of the solidand broken lines in FIG. 8 b. Consequently, the vibrational portion 63is capable of extending and contracting in the length direction.

FIG. 9 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the fourth embodiment of the present invention. The quartzcrystal unit 170 comprises a contour mode quartz crystal resonator 70 ora thickness shear mode quartz crystal resonator 70, a case 71 and a lid72. In more detail, the resonator 70 is mounted at a mounting portion 74of the case 71 by conductive adhesives 76 or solder. Also, the case 71and the lid 72 are connected through a connecting member 73. Forexample, the contour mode resonator 70 in this embodiment is the sameresonator as one of the flexural mode, quartz crystal tuning forkresonators 10 and 45 described in detail in FIG. 4-FIG. 7. Also, in thisembodiment, circuit elements are connected at outside of the quartzcrystal unit to get a quartz crystal oscillator. Namely, only the quartzcrystal tuning fork resonator is housed in the unit and also, it ishoused in the unit in vacuum. In this embodiment, the quartz crystalunit of a surface mounting type is shown, but the quartz crystal tuningfork resonator may be housed in a tubular type, namely a quartz crystalunit of the tubular type. Also, instead of the flexural mode, quartzcrystal tuning fork resonator and the thickness shear mode quartzcrystal resonator, one of a length-extensional mode quartz crystalresonator, a width-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator which are a contour mode resonator,respectively, or a SAW (Surface Acoustic Wave) resonator may be housedin the unit. For example, FIG. 19 shows a top view (a) and a C-C′cross-sectional view (b) of a vibrational portion 555 of a thicknessshear mode quartz crystal resonator 550. The resonator 550 has adimension of a length L₀, a width W₀ and a thickness T₀, and the lengthL₀ and the width W₀ is less than 2.4 mm and 1.6 mm, respectively, toachieve a smaller quartz crystal unit and to get a small seriesresistance R₁. Also, electrodes 556 and 557 are disposed on upper andlower surfaces so that the electrodes are opposite each other. In orderto get a good frequency temperature behaviour at a room temperature atleast, the resonator 550 has a cut angle within a range of YXl(34° to36°) according to an expression of the IEEE notation. In addition, thepresent invention is not limited to the quartz crystal unit having thecontour mode quartz crystal resonator or the thickness shear mode quartzcrystal resonator in this embodiment, for example, the present inventionalso includes a quartz crystal unit having a piezoelectric filter, e.g.a SAW piezoelectric filter or a piezoelectric sensor, e.g. an angularvelocity piezoelectric sensor. Namely, the piezoelectric materialcomprises one of LiTaO₃, LiNbO₃, GaPO₄, and so on which belong to atrigonal system in crystallographic classification.

In addition, a member of the case and the lid is ceramics or glass and ametal or glass, respectively, and a connecting member is a metal orglass with low melting point. Also, a relationship of the resonator, thecase and the lid described in this embodiment is applied to a quartzcrystal oscillator of the present invention which will be described inFIG. 10.

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fifth embodiment of thepresent invention. The quartz crystal oscillator 190 comprises a quartzcrystal oscillating circuit, a case 91 and a lid 92. In this embodiment,circuit elements constructing the oscillating circuit are housed in aquartz crystal unit comprising a contour mode quartz crystal resonator90 or a thickness shear mode quartz crystal resonator 90, the case 91and the lid 92. Also, the oscillating circuit of this embodimentcomprises an amplifier 98 including a feedback resistor, the resonator90, capacitors (not shown here) and a drain resistor (not shown here),and a CMOS inverter is used as the amplifier 98.

In addition, in this embodiment, the resonator 90 is mounted at amounting portion 94 of the case 91 by conductive adhesives 96 or solder.As described above, the amplifier 98 is housed in the quartz crystalunit and mounted at the case 91. Also, the case 91 and the lid 92 areconnected through a connecting member 93. For example, the contour moderesonator 90 of this embodiment is the same as one of the flexural mode,quartz crystal tuning fork resonators 10 and 45 described in detail inFIG. 4-FIG. 7. Also, instead of the flexural mode, quartz crystal tuningfork resonator and the thickness shear mode quartz crystal resonator,one of a length-extensional mode quartz crystal resonator, awidth-extensional mode quartz crystal resonator and a Lame mode quartzcrystal resonator which are a contour mode resonator, respectively, or aSAW (Surface Acoustic Wave) resonator, or a torsional mode quartzcrystal resonator may be housed in the unit. In addition, the torsionalmode resonator has a tuning fork shape with a tuning fork base havingcut portions and tuning fork tines connected to the tuning fork base.The tuning fork tines vibrate in a torsional mode of an inverse. Inaddition, a length of each of the tuning fork tines is within a range of0.6 mm to 2.1 mm, preferably, 0.65 mm to 1.85 mm, so that the torsionalresonator capable of vibrating in a fundamental mode can be obtainedwith a frequency higher than 150 kHz and less than 750 kHz.

Likewise, in this embodiment, a piece of flexural mode, quartz crystaltuning fork resonator is housed in the unit, but the present inventionalso includes a quartz crystal unit having a plurality of flexural mode,quartz crystal tuning fork resonators, each of which has tuning forktines and a tuning fork base, and at least two of the plurality ofresonators are connected electrically in parallel. In addition, the atleast two resonators may be an individual resonator or may be individualresonators that are formed integrally at each tuning fork base through aconnecting portion. For example, the at least two resonators comprisestwo individual resonators, and the two individual resonators are formedso that one of the two individual resonators has a groove in at leastone of upper and lower faces of the tuning fork tines, and the other hasno groove in at least one of upper and lower faces of the tuning forktines to get a different turn over temperature point each other. Inaddition, a shape and a dimension of the groove and the tuning forktines may be changed to get the different turn over temperature pointeach other.

Next, a method for manufacturing a quartz crystal oscillator, whichconstructs an electronic apparatus of the present invention, isdescribed in detail, according to the manufacturing steps.

FIG. 11 shows an embodiment of a method for manufacturing a quartzcrystal oscillator, which constructs an electronic apparatus of thepresent invention and a step diagram embodying the present invention.The signs of S-1 to S-12 are the step numbers. First, S-1 shows across-sectional view of a quartz crystal wafer 140. Next, in S-2 metalfilm 141, for example, chromium and gold on the chromium are,respectively, disposed on upper and lower faces of the quartz crystalwafer 140 by an evaporation method or a spattering method. In addition,resist 142 is spread on said metal film 141 in S-3, and after the metalfilm 141 and the resist 142 were removed except those of tuning forkshape by a photo-lithographic process and an etching process, the tuningfork shape with tuning fork tines 143, 144 and a tuning fork base 145,as be shown in S-4, is integrally formed by a chemical etching processso that an oscillation frequency of a quartz crystal resonator of thetuning fork shape is in the range of 34.1 kHz to 38.7 kHz, preferably,34.1 kHz to 36.9 kHz. When the tuning fork shape is formed, cut portionsmay be formed at the tuning fork base. In other words, the tuning forkshape and the cut portions are formed simultaneously. In FIG. 11, theformation of a piece of tuning fork shape is shown, but, a number oftuning fork shapes are actually formed in a piece of quartz crystalwafer.

Similar to the steps of S-2 and S-3, metal film and resist are spreadagain on the tuning fork shape of S-4 and grooves 146, 147, 148 and 149each of which has two step difference portions along the lengthdirection of the tuning fork tines, are formed at the tuning fork tines143, 144 by an photo-lithographic process and an etching process so thatthe oscillation frequency of the quartz crystal resonator of the tuningfork shape having the grooves is in the range of 32.78 kHz to 34.4 kHz,preferably, 32.78 kHz to 33.85 kHz and a turn over temperature point of(a turning point) the quartz crystal resonator thereof is in the rangeof 15° C. to 35° C., preferably, 18° C. to 30° C. to get a smallfrequency deviation in the vicinity of room temperature because thequartz crystal resonator of the tuning fork shape has a parabolic curvein frequency temperature behaviour, and the shape of S-5 is obtainedafter all of the resist and the metal film are removed. In addition,metal film and resist are spread again on the shape of S-5 andelectrodes which are of opposite electrical polarity, are disposed onsides of the tines and inside the grooves thereof, as shown in S-6.

Namely, electrodes 150, 153 disposed on the sides of the tuning forktine 143 and electrodes 155, 156 disposed inside the grooves 148, 149 ofthe tuning fork tine 144 have the same electrical polarity. Similarly,electrodes 151, 152 disposed inside the grooves 146, 147 of the tuningfork tine 143 and electrodes 154, 157 disposed on the sides of thetuning fork tine 144 have the same electrical polarity. Two electrodeterminals are, therefore, constructed. In more detail, when analternating current (AC) voltage is applied between the terminals, thetuning fork tines vibrate in a flexural mode of an inverse phase becausesaid electrodes disposed on step difference portions of the grooves andthe electrodes disposed opposite to the said electrodes have oppositeelectrical polarity. In the step of S-6, a piece of quartz crystaltuning fork resonator, capable of vibrating in a flexural mode is shownin the quartz crystal wafer, but a number of quartz crystal tuning forkresonators are actually formed in the wafer. When the grooves are formedat the tuning fork tines, the oscillation frequency of the resonator ofthe tuning fork shape becomes lower than that of the resonator with nogroove, and the quantity of a change of the oscillation frequency isdependent on a number of the grooves, a groove width, a groove lengthand a groove depth. In this embodiment, the oscillation frequency of theresonator of the tuning fork shape is adjusted in the quartz crystalwafer by forming a metal film on each of at least two of the upper andlower faces of each of the tuning fork tines so that the oscillationfrequency is lower than 32.73 kHz, preferably, less than 32.69 kHz, morepreferably, greater than 31.6 kHz and less than 32.69 kHz and the metalfilm is formed after or before the step of S-6, namely, after or beforethe two electrode terminals are formed to drive the resonator of thetuning fork shape. In more detail, the metal film on each of at leasttwo of the upper and lower faces of each of the tuning fork tines toadjust the oscillation frequency is formed after the tuning fork shapeis formed (after the step of S-4) and before the grooves are formed(before the step of S-5) or is formed after the grooves are formed(after the step of S-5) and before the electrodes are disposed (beforethe step of S-6) or is formed after the electrodes are disposed (afterthe step of S-6) and before the resonator of the tuning fork shape ismounted on a mounting portion of a case (before the step of S-7 or S-8).Also, when the resonator of the tuning fork shape housed in a unithaving a case and a lid has no groove at the tuning fork tines, anoscillation frequency of the resonator of the tuning fork shape formedin a quartz wafer by etching is in the range of 32.78 kHz to 34.4 kHz,preferably, 32.78 kHz to 33.85 kHz. In addition, a metal film on each ofat least two of the upper and lower faces of each of the tuning forktines is formed to adjust the oscillation frequency of the resonator sothat the oscillation frequency is lower than 32.73 kHz, preferably, lessthan 32.69 kHz, more preferably, greater than 31.6 kHz and less than32.69 kHz, and the metal film is formed after or before the electrodes(two electrode terminals) are formed to drive the resonator of thetuning fork shape. In more detail, the metal film on each of at leasttwo of the upper and lower faces of each of the tuning fork tines isformed after the tuning fork shape is formed and before the electrodesare disposed or is formed after the electrodes are disposed and beforethe tuning fork shape is mounted on a mounting portion of a case.According to the present invention, the metal film on each of at leasttwo of the upper and lower faces of each of the tuning fork tines may beformed before the tuning fork shape is formed.

In addition, a resonance (oscillation) frequency for said resonators isadjusted by a separate step of at least twice and the first adjustmentof resonance frequency for said resonators is performed in the quartzcrystal wafer by a laser method or an evaporation method or an ionetching method so that a frequency deviation of said resonators iswithin a range of −9000 PPM to +5000 PPM (Parts Per Million),preferably, within a range of −9000 PPM to +100 PPM, more preferably,within a range of −2300 PPM to +100 PPM to a nominal frequency of 10 kHzto 200 kHz, e.g. 32.768 kHz. The adjustment of frequency by the laser orion etching method is performed by trimming mass (at least one of themetal films) disposed on tuning fork tines and the adjustment offrequency by the evaporation method is performed by adding mass (ametal) on tuning fork tines. Namely, those methods can change theresonance (oscillation) frequency of said resonators. Also, theresonators formed in the quartz crystal wafer are inspected therein andwhen there is a failure resonator, it is removed from the wafer orsomething is marked on it or it is remembered by a computer.

In this embodiment, the tuning fork shape is formed from the step of S-3and after that, the grooves are formed at the tuning fork tines, namely,the tuning fork tines are formed before the grooves are formed, but thisinvention is not limited to said embodiment, for example, the groovesare first formed from the step of S-3 and after that, the tuning forkshape may be formed, namely, the grooves are formed before the tuningfork tines are formed. Also, the tuning fork shape and the grooves maybe formed simultaneously, namely, the tuning fork tines and the groovesare formed simultaneously. When the tuning fork tines and the groovesare formed simultaneously, for example, a portion between the tuningfork tines is first etched so that the portion has a groove and athickness of the portion is less than seven tenths, preferably, one halfof a thickness of the quartz crystal wafer to get a required oscillationfrequency and a required turn over temperature point, and after that theportion and the groove are formed simultaneously by etching the quartzcrystal wafer. For example, when the thickness of the quartz crystalwafer is in the range of 0.07 mm to 0.12 mm, the thickness of the baseportion is less than 0.05 mm, preferably, 0.035 mm, more preferably,0.005 mm. Namely, the portion has the groove as deep as possible to getthe required oscillation frequency and the required turn overtemperature point. Moreover, when the tuning fork base has cut portions,the portion between the tuning fork tines and the cut portions areformed simultaneously. In addition, when the tuning fork base has aframe portion, the tuning fork shape and the frame portion are formedsimultaneously. According to the present invention, when the tuning forkbase has at least one of cut portions and a frame portion, the at leastone is formed simultaneously with the tuning fork shape. Moreover, forexample, when a groove having a plurality of stepped portions is formedin each of upper and lower faces of the tuning fork tines, the groovemay be formed simultaneously with at least one of the cut portions andthe frame portion. In addition, at least one of the cut portions may beformed in a step different from at least one of the steps of forming thetuning fork tines and forming the grooves at the tuning fork tines.Namely, the at least one of the cut portions is formed before or afterat least one of the tuning fork tines and the grooves is formed. Similarto this, the frame portion may be formed in a step different from atleast one of the steps of forming the tuning fork tines and forming thegrooves at the tuning fork tines. Namely, the frame portion is formedbefore or after at least one of the tuning fork tines and the grooves isformed. In addition, at least one of the metal films on the upper andlower faces of each of the tuning fork tines to adjust the oscillationfrequency of the resonator of the tuning fork shape may be formed beforethe step of forming the tuning fork tines.

There are two methods of A and B in the following step, as be shown byarrow signs. For the step of A, the tuning fork base 145 of the formedflexural mode, quartz crystal tuning fork resonator 160 is first mountedon mounting portion 159 of a case 158 by conductive adhesives 161 orsolder, as be shown in S-7. Next, the second adjustment of resonance(oscillation) frequency for the resonator 160 is performed by laser 162or evaporation or ion etching method in S-8 so that a frequencydeviation is within a range of −100 PPM to +100 PPM to the nominalfrequency of 10 kHz to 200 kHz, e.g. 32.768 kHz. Finally, the case 158and a lid 163 are connected via glass 164 with the low melting point ora metal in S-9. In this case, the connection of the case and the lid isperformed in vacuum because the case 158 has no hole to close it invacuum.

In addition, though it is not visible in FIG. 11, the third frequencyadjustment may be performed by laser after the step of the connection ofS-9 to get a small frequency deviation to the nominal frequency when amaterial of the lid is glass. As a result of which it is possible to getthe resonator with the frequency deviation which is within a range of−50 PPM to +50 PPM to the nominal frequency of 10 kHz to 200 kHz, e.g.32.768 kHz. Namely, the nominal frequency, capable of vibrating in afundamental mode is less than 200 kHz. In this step, when the thirdfrequency adjustment is performed, a/an resonance (oscillation)frequency of said resonators is adjusted so that the frequency deviationby the second frequency adjustment is within a range of −1500 PPM to+1500 PPM, preferably, −950 PPM to +950 PPM to the nominal frequency,e.g. 32.768 kHz.

For the step of B, the tuning fork base 145 of the formed resonator 160is first mounted on a mounting portion 159 of a case 165 by conductiveadhesives 161 or solder in S-10, in addition, in S-11 the case 165 and alid 163 are connected by the same way as that of S-9, in more detail,after the resonator was mounted on the mounting portion of the case orafter the resonator was mounted at the mounting portion, and the caseand the lid were connected, the second adjustment of resonance(oscillation) frequency is performed so that a frequency deviation isgenerally within a range of −100 PPM to +100 PPM to a nominal frequencyof 10 kHz to 200 kHz, e.g. 32.768 kHz in vacuum, but, it may be within awider range, for example, −950 PPM to +950 PPM when the third frequencyadjustment as will be shown as follows, is performed. Finally, a hole167 constructed at the case 165 is closed in vacuum using such a metal166 as solder or glass with the low melting point in S-12.

Also, similar to the step of A, the third adjustment of resonance(oscillation) frequency may be performed by laser after the step of S-12to get a small frequency deviation to the nominal frequency. As a resultof which it is possible to get the resonator with the frequencydeviation which is within a range of −50 PPM to +50 PPM to the nominalfrequency, e.g. 32.768 kHz. Thus, a frequency deviation of theresonators in the case of A and B is finally within a range of −100 PPMto +100 PPM at most. Also, the second frequency adjustment may beperformed after the case and the lid were connected and the hole wasclosed in vacuum. In addition, the hole is constructed at the case, butmay be constructed at the lid. Also, the frequency adjustment of thepresent invention is performed in vacuum or inert gas such as nitrogengas or atmosphere, and the values described above are values in vacuum.

Therefore, the flexural mode, quartz crystal tuning fork resonators andthe quartz crystal units manufactured by the above-described method areminiaturized and realized with a small series resistance R₁, a highquality factor Q₁ and low price.

Moreover, in the above-described embodiment, though the first frequencyadjustment of the resonators is performed in the quartz crystal waferand at the same time, when there is a failure resonator, something ismarked on it or it is removed from the quartz crystal wafer, but thepresent invention is not limited to this, namely, the present inventionmay include the step to inspect the flexural mode, quartz crystal tuningfork resonators formed in the quartz crystal wafer therein, in otherwords, the step to inspect whether there is a failure resonator or notin the quartz crystal wafer. When there is a failure resonator in thewafer, something is marked on it or it is removed from the wafer or itis remembered by a computer. By including the step, it can increase theyield because it is possible to find out the failure resonator in anearly step and the failure resonator does not go to the next step. As aresult of which low priced flexural mode, quartz crystal tuning forkresonators can be provided with excellent electrical characteristics.

In this embodiment, the frequency adjustment is performed three times bya separate step, but may be performed at least twice by a separate step.For example, the third frequency adjustment may be omitted. In addition,in order to construct a quartz crystal oscillator, two electrodeterminals of the resonators are connected electrically to an amplifier,capacitors and resistors. In other words, a quartz crystal oscillatingcircuit is constructed and connected electrically so that anamplification circuit comprises a CMOS inverter and a feedback resistorand a feedback circuit comprises a flexural mode, quartz crystal tuningfork resonator, a drain resistor, a capacitor of a gate side and acapacitor of a drain side. Also, the third frequency adjustment may beperformed after the quartz crystal oscillating circuit was constructedin a quartz crystal unit.

Likewise, the flexural mode quartz crystal resonator of a tuning forktype has two tuning fork tines in the present embodiments, butembodiments of the present invention include tuning fork tines more thantwo. In addition, the quartz crystal tuning fork resonators of thepresent embodiments are housed in a package (unit) of a surface mountingtype comprising a case and a lid, but may be housed in a package of atubular type.

In addition, for the tuning fork resonators constructing the quartzcrystal oscillators of the first embodiment to the fourth embodiment ofthe present invention, the resonators are provided so that a capacitanceratio r₁ of a fundamental mode vibration gets smaller than a capacitanceratio r₂ of a second overtone mode vibration, in order to obtain afrequency change of the fundamental mode vibration larger than that ofthe second overtone mode vibration, versus the same change of a value ofload capacitance C_(L). Namely, a variable range of a frequency of thefundamental mode vibration gets wider than that of the second overtonemode vibration.

In more detail, for example, when C_(L)=18 pF and the C_(L) changes in 1pF, the frequency change of the fundamental mode vibration becomeslarger than that of the second overtone mode vibration because thecapacitance ratio r₁ is smaller than the capacitance ratio r₂.Therefore, there is a remarkable effect for the fundamental modevibration, such that the resonators can be provided with the frequencyvariable in the wide range, even when the value of load capacitanceC_(L) changes slightly. Accordingly, when a variation of the samefrequency is required, the number of capacitors which are used in thequartz crystal oscillators decreases because the frequency change versusload capacitance 1 pF becomes large, as compared with that of the secondovertone mode vibration. As a result, the low priced oscillators can beprovided.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode vibration and a second overtone modevibration in the electrical equivalent circuit of the resonator. Inaddition, the flexural mode, quartz crystal tuning fork resonator has aquality factor Q₁ for the fundamental mode vibration and a qualityfactor Q₂ for the second overtone mode vibration.

In detail, the tuning fork resonator of this embodiment is provided sothat the influence on resonance frequency of the fundamental modevibration by the shunt capacitance becomes smaller than that of thesecond overtone mode vibration by the shunt capacitance, namely, so thatit satisfies a relationship of S₁=r₁/2Q₁ ²<S₂=r₂/2Q₂ ², preferably,S₁<S₂/2. As a result, the tuning fork resonator, capable of vibrating inthe fundamental mode and having a high frequency stability can beprovided because the influence on the resonance frequency of thefundamental mode vibration by the shunt capacitance becomes so extremelysmall as it can be ignored. Also, the present invention replaces r₁/2Q₁² with S₁ and r₂/2Q₂ ² with S₂, respectively, and here, S₁ and S₂ arecalled “a stable factor of frequency” of the fundamental mode vibrationand the second overtone mode vibration.

In addition, when a power source is applied to the quartz crystaloscillating circuit, at least one oscillation which satisfies anamplitude condition and a phase condition of vibration starts in thecircuit, and a spent time to get to about ninety percent of the steadyamplitude of the vibration is called “rise time”. Namely, the shorterthe rise time becomes, the easier the oscillation becomes. When risetime t_(r1) of the fundamental mode vibration and rise time t_(r2) ofthe second overtone mode vibration in the circuit are taken, t_(r1) andt_(r2) are given by t_(r1)=kQ₁/(ω₁(−1+|−RL₁|/R₁)) andt_(r2)=kQ₂/(ω₂(−1+|−RL₂|/R₂)), respectively, where k is constant and ω₁and ω₂ are an angular frequency for the fundamental mode vibration andthe second overtone mode vibration, respectively.

From the above-described relation, it is possible to obtain the risetime t_(r1) of the fundamental mode vibration less than the rise timet_(r2) of the second overtone mode vibration. As an example, whenresonance (oscillation) frequency of a flexural mode, quartz crystaltuning fork resonator is about 32.768 kHz for a fundamental modevibration and the resonator has a value of W₂/W=0.5, t₁/t=0.34 andl₁/=0.48, though there is a distribution in production, as an example,the resonator has a value of Q₁=62,000 and Q₂=192,000, respectively. Inthis embodiment, Q₂ has a value of about three times of Q₁. Accordingly,to obtain the t_(r1) less than the t_(r2), it is necessary to satisfy arelationship of |−RL₁|/R₁>2|−RL₂|/R₂−1 by using a relation of ω₂=6ω₁approximately. Also, according to this invention, the relationship isnot limited to the quartz crystal oscillating circuit comprising theresonator in this embodiment, but this invention also includes allquartz crystal oscillating circuits to satisfy the relationship. Byconstructing the oscillating circuit like this, a quartz crystaloscillator with the flexural mode, quartz crystal tuning fork resonatorcan be provided with a short rise time. In other words, an output signalof the oscillator has an oscillation frequency of the fundamental modevibration of the resonator and is outputted through a buffer circuit.Namely, the second overtone mode vibration can be suppressed in theoscillating circuit. In this embodiment, the resonator has also a valueof r₁=320 and r₂=10,600 as an example. According to this invention, r₁has a value of 210 to 520.

The above-described quartz crystal resonators are formed by at least onemethod of chemical, mechanical and physical methods. The mechanicalmethod, for example, uses a particle such as GC#1000 and the physicalmethod, for example, uses atom or molecule. Therefore, these methods arecalled “a particle method” here. In addition, the present invention isnot limited to the resonators described above, but includes such apiezoelectric resonator for sensing pressure as a flexural mode, tuningfork resonator, a torsional mode resonator, a thickness shear moderesonator, SAW resonator and so on. In detail, there is a relationshipbetween the pressure and an oscillation frequency of the resonators or aseries resistance R₁ thereof. In more detail, the higher the pressurebecomes, the lower the oscillation frequency becomes or the higher theseries resistance R₁ becomes. Namely, since the oscillation frequency ofthe resonators or the series resistance thereof changes by a change ofthe pressure, the pressure is measured from the relationship.

Thus, the electronic apparatus of this invention comprising a displayportion and a quartz crystal oscillator at least may operate normallybecause the quartz crystal oscillator comprises the quartz crystaloscillating circuit with a high frequency stability, namely, a highfrequency reliability.

As described above, it will be easily understood that the electronicapparatus comprising the quartz crystal oscillator comprising the quartzcrystal oscillating circuit having the flexural mode, quartz crystaltuning fork resonator with novel shapes, the novel electrodeconstruction and excellent electrical characteristics, according to thepresent invention, may have the outstanding effects. Similar to this, itwill be easily understood that the electronic apparatus comprising thequartz crystal oscillator comprising the quartz crystal oscillatingcircuit having the length-extensional mode quartz crystal resonator withthe novel cutting angle and the novel shape, according to the presentinvention, may have also the outstanding effect. In addition to this,while the present invention has been shown and described with referenceto preferred embodiments thereof, it will be understood by those skilledin the art that the changes in shape and electrode construction can bemade therein without departing from the spirit and scope of the presentinvention.

1. A quartz crystal unit comprising: a quartz crystal resonator; a casehaving a mounting portion; and a lid; wherein the quartz crystalresonator comprises a quartz crystal tuning fork resonator having aquartz crystal tuning fork shape including a quartz crystal tuning forkbase and first and second quartz crystal tuning fork tines connected tothe quartz crystal tuning fork base, each of the first and second quartzcrystal tuning fork tines having opposite main surfaces and oppositeside surfaces; wherein at least one groove having at least threesurfaces including a first surface opposite at least one of the oppositeside surfaces and a second surface connected to the first surfacethrough a third surface is formed in at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines; wherein an electrode is disposed on at least one of the first andsecond surfaces of the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines and on the at least one of the opposite sidesurfaces of each of the first and second quartz crystal tuning forktines so that the electrode disposed on the at least one of the oppositeside surfaces of the first quartz crystal tuning fork tine has the sameelectrical polarity as an electrical polarity of the electrode disposedon the at least one of the first and second surfaces of the at least onegroove formed in the at least one of the opposite main surfaces of thesecond quartz crystal tuning fork tine and the electrode disposed on theat least one of the first and second surfaces of the at least one grooveformed in the at least one of the opposite main surfaces of the firstquartz crystal tuning fork tine has an electrical polarity opposite tothe electrical polarity of the electrode disposed on the at least one ofthe first and second surfaces of the at least one groove formed in theat least one of the opposite main surfaces of the second quartz crystaltuning fork tine, the quartz crystal tuning fork resonator vibrating ina flexural mode of an inverse phase; wherein the quartz crystal tuningfork resonator has a quality factor Q₂, a capacitance ratio r₂ and amerit value M₂ of a second overtone mode of vibration, the merit valueM₂ being defined by the ratio (Q₂/r₂), each of the quartz crystal tuningfork shape, the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines and the electrode disposed on the at least one of thefirst and second surfaces of the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines having a dimension; wherein thedimension of each of the quartz crystal tuning fork shape, the at leastone groove formed in the at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines and theelectrode disposed on the at least one of the first and second surfacesof the at least one groove formed in the at least one of the oppositemain surfaces of each of the first and second quartz crystal tuning forktines is determined so that the merit value M₂ of the second overtonemode of vibration of the quartz crystal tuning fork resonator is lessthan 30; wherein the quartz crystal tuning fork resonator is mounted onthe mounting portion of the case; and wherein the lid is connected tothe case.
 2. A quartz crystal unit according to claim 1; wherein thequartz crystal tuning fork resonator has a quality factor Q₁, acapacitance ratio r₁ and a merit value M₁ of a fundamental mode ofvibration, the merit value M₁ being defined by the ratio (Q₂/r₂); andwherein the dimension of each of the quartz crystal tuning fork shape,the at least one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines and the electrode disposed on the at least one of the first andsecond surfaces of the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines is determined so that the merit value M₁ ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is greater than
 65. 3. A quartz crystal unit according toclaim 1; wherein the quartz crystal tuning fork resonator has a qualityfactor Q₁, a capacitance ratio r₁ and a stable factor S₁ of thefundamental mode of vibration, and a stable factor S₂ of the secondovertone mode of vibration, the stable factor s₁ being defined by r₁/2Q₁² and the stable factor S₂ being defined by r₂/2Q₂ ²; and wherein thedimension of each of the quartz crystal tuning fork shape, the at leastone groove formed in the at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines and theelectrode disposed on the at least one of the first and second surfacesof the at least one groove formed in the at least one of the oppositemain surfaces of each of the first and second quartz crystal tuning forktines is determined so that the stable factor S₁ of the fundamental modeof vibration of the quartz crystal tuning fork resonator is less thanthe stable factor S₂ of the second overtone mode of vibration thereofand the capacitance ratio r₁ of the fundamental mode of vibration of thequartz crystal tuning fork resonator is less than the capacitance ratior₂ of the second overtone mode of vibration thereof.
 4. A quartz crystaloscillator comprising: at least one quartz crystal oscillating circuitcomprised of an amplifier; at least one resistor; a plurality ofcapacitors; and a quartz crystal unit according to claim 1; wherein thequartz crystal tuning fork resonator of the quartz crystal unit isconnected to the amplifier, the at least one resistor and thecapacitors.
 5. A quartz crystal oscillator according to claim 4; whereinthe case is a ceramics case having an interior space and a mountingportion in the interior space; wherein the quartz crystal tuning forkresonator is mounted on the mounting portion in the interior space ofthe ceramics case by a conductive adhesive or a solder; wherein the lidis a metal lid or a glass lid; wherein the metal lid or the glass lid isconnected to the ceramics case to cover an open end of the ceramicscase; wherein the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines has a length; wherein the quartz crystal tuning forkresonator has an overall length, and a series resistance R₁ of afundamental mode of vibration and a series resistance R₂ of the secondovertone mode of vibration; wherein each of the length of the at leastone groove formed in the at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines and theoverall length of the quartz crystal tuning fork resonator is determinedso that R₁ is less than 0.86R₂; wherein the quartz crystal tuning forkresonator has a capacitance ratio r₁ of the fundamental mode ofvibration; wherein the dimension of each of the quartz crystal tuningfork shape, the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines and the electrode disposed on the at least one of thefirst and second surfaces of the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines is determined so that the quartzcrystal unit has the capacitance ratio r₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator in the range of210 to 520; and wherein the quartz crystal tuning fork resonator isformed in a quartz crystal wafer within a range of 0.05 mm to 0.15 mm.6. A quartz crystal oscillator according to claim 4; wherein the quartzcrystal tuning fork resonator has a quality factor Q₁, a capacitanceratio r₁ and a stable factor S₁ of a fundamental mode of vibration, anda stable factor S₂ of the second overtone mode of vibration, the stablefactor S₁ being defined by r₁/2Q₁ ² and the stable factor S₂ beingdefined by r₂/2Q₂ ²; and wherein the dimension of each of the quartzcrystal tuning fork shape, the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines and the electrode disposed on the atleast one of the first and second surfaces of the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines is determined so thatthe stable factor S₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is less than the stable factor S₂ of thesecond overtone mode of vibration thereof and the capacitance ratio r₂of the second overtone mode of vibration thereof is greater than 1500.7. A quartz crystal oscillator according to claim 4; wherein theopposite main surfaces have a first main surface and a second mainsurface; wherein the quartz crystal tuning fork resonator has anoscillation frequency; and wherein the at least one groove comprises agroove having a base portion and a length less than 1.29 mm formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is greater than orequal to a distance in the width direction of the groove measured froman outer edge of the groove to an outer edge of the corresponding one ofthe first and second quartz crystal tuning fork tines, and a thicknessof the base portion of the groove formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is less than 0.05 mm and the oscillation frequency of the quartzcrystal tuning fork resonator is in the range of 32.78 kHz to 34.4 kHz.8. An electronic apparatus comprising: at least one quartz crystaloscillating circuit comprised of an amplifier; at least one resistor; aplurality of capacitors; and a quartz crystal unit according to claim 1;wherein the quartz crystal tuning fork resonator of the quartz crystalunit is connected to the amplifier, the at least one resistor and thecapacitors; and wherein an output signal of the at least one quartzcrystal oscillating circuit comprised of the quartz crystal unit is aclock signal for use in operation of the electronic apparatus.
 9. Anelectronic apparatus according to claim 8; further comprising a displayportion; wherein the at least one quartz crystal oscillating circuit hasa first quartz crystal oscillating circuit comprised of a firstamplifier, at least one first resistor, a plurality of first capacitorsand a first quartz crystal unit having the quartz crystal tuning forkresonator; wherein the quartz crystal tuning fork resonator of the firstquartz crystal unit is connected to the first amplifier, the at leastone first resistor and the first capacitors; wherein the quartz crystaltuning fork resonator has a shunt capacitance and a fundamental mode ofvibration; wherein a frequency difference of a mechanical resonancefrequency independent on the shunt capacitance of the fundamental modeof vibration of the quartz crystal tuning fork resonator and a resonancefrequency dependent on the shunt capacitance of the fundamental mode ofvibration thereof is defined by Δf₁; wherein a frequency difference of amechanical resonance frequency independent on the shunt capacitance ofthe second overtone mode of vibration of the quartz crystal tuning forkresonator and a resonance frequency dependent on the shunt capacitanceof the second overtone mode of vibration thereof is defined by Δf₂;wherein the dimension of each of the quartz crystal tuning fork shape,the at least one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines and the electrode disposed on the at least one of the first andsecond surfaces of the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines is determined so that the frequencydifferences Δf_(t) of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is less than the frequency difference Δf₂of the second overtone mode of vibration thereof, and the capacitanceratio r₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than the capacitance ratio r₂ of thesecond overtone mode of vibration thereof; wherein an output signal ofthe first quartz crystal oscillating circuit comprised of the firstquartz crystal unit is a clock signal for use in operation of theelectronic apparatus to display time information at the display portion,the clock signal having an oscillation frequency of the fundamental modeof vibration of the quartz crystal tuning fork resonator and theoscillation frequency of the fundamental mode of vibration thereof beingabout 32.768 kHz with a frequency deviation within a range of −100 ppmto +100 ppm; wherein the at least one quartz crystal oscillating circuithas a second quartz crystal oscillating circuit comprised of a secondamplifier, at least one second resistor, a plurality of secondcapacitors and a second quartz crystal unit having a thickness shearmode quartz crystal resonator; wherein the thickness shear mode quartzcrystal resonator of the second quartz crystal unit is connected to thesecond amplifier, the at least one second resistor and the secondcapacitors; and wherein an output signal of the second quartz crystaloscillating circuit comprised of the second quartz crystal unit is aclock signal for use in operation of the electronic apparatus.
 10. Anelectronic apparatus according to claim 8; further comprising a displayportion; wherein the at least one quartz crystal oscillating circuit hasa first quartz crystal oscillating circuit comprised of a firstamplifier, at least one first resistor, a plurality of first capacitorsand a first quartz crystal unit having the quartz crystal tuning forkresonator; wherein the quartz crystal tuning fork resonator of the firstquartz crystal unit is connected to the first amplifier, the at leastone first resistor and the first capacitors; wherein the quartz crystaltuning fork resonator has a quality factor Q₁, a capacitance ratio r₁and a stable factor S₁ of a fundamental mode of vibration and a stablefactor S₂ of the second overtone mode of vibration, the stable factor S₁being defined by r₁/2Q₁ ² and the stable factor S₂ being defined byr₂/2Q₂ ²; wherein the dimension of each of the quartz crystal tuningfork shape, the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines and the electrode disposed on the at least one of thefirst and second surfaces of the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines is determined so that the stable factorS₁ of the fundamental mode of vibration of the quartz crystal tuningfork resonator is less than the stable factor S₂ of the second overtonemode of vibration thereof; and wherein an output signal of the firstquartz crystal oscillating circuit comprised of the first quartz crystalunit is a clock signal for use in operation of the electronic apparatusto display time information at the display portion.
 11. An electronicapparatus according to claim 10; wherein the at least one quartz crystaloscillating circuit has a second quartz crystal oscillating circuitcomprised of a second amplifier, at least one second resistor, aplurality of second capacitors and a second quartz crystal unit having athickness shear mode quartz crystal resonator; wherein the thicknessshear mode quartz crystal resonator of the second quartz crystal unit isconnected to the second amplifier, the at least one second resistor andthe second capacitors; wherein an output signal of the second quartzcrystal oscillating circuit comprised of the second quartz crystal unitis a clock signal for use in operation of the electronic apparatus; andwherein the dimension of each of the quartz crystal tuning fork shape,the at least one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines and the electrode disposed on the at least one of the first andsecond surfaces of the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines is determined so that the capacitance ratio r₁of the fundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof.
 12. An electronic apparatus according toclaim 11; wherein the dimension of each of the quartz crystal tuningfork shape, the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines and the electrode disposed on the at least one of thefirst and second surfaces of the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines is determined so that the capacitanceratio r₂ of the second overtone mode of vibration of the quartz crystaltuning fork resonator is greater than 1500; wherein the opposite mainsurfaces have a first main surface and a second main surface; whereinthe at least one groove comprises a groove having a length formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is greater than orequal to a distance in the width direction of the groove measured froman outer edge of the groove to an outer edge of the corresponding one ofthe first and second quartz crystal tuning fork tines and less than aspaced-apart distance between the first and second quartz crystal tuningfork tines, and a length of the groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is within a range of 40% to 80% of a length of each ofthe first and second quartz crystal tuning fork tines and less than 1.29mm; wherein the quartz crystal tuning fork resonator has an overalllength, and a series resistance R₁ of the fundamental mode of vibrationand a series resistance R₂ of the second overtone mode of vibration;wherein each of the length of the groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines and the overall length of the quartz crystal tuningfork resonator is determined so that R₁ is less than 0.86R₂; wherein thecase is a ceramics case having an interior space and a mounting portionin the interior space, and a through-hole; wherein the lid is a metallid or a glass lid; wherein the quartz crystal tuning fork base has afirst base portion including a first width W₅ and a second base portionincluding a second width W₆ greater than or equal to the first width W₅so that two cut portions are formed between the first and second baseportions of the quartz crystal tuning fork base, each of the first andsecond quartz crystal tuning fork tines being connected to the firstbase portion of the quartz crystal tuning fork base; wherein the secondbase portion of the quartz crystal tuning fork base is mounted on themounting portion in the interior space of the ceramics case by aconductive adhesive or a solder; wherein the metal lid or the glass lidis connected to the ceramics case to cover an open end of the ceramicscase; wherein a metal or a glass is disposed in the through-hole of theceramics case to close the through-hole thereof in a vacuum; and whereinthe clock signal for use in operation of the electronic apparatus todisplay time information at the display portion has an oscillationfrequency of the fundamental mode of vibration of the quartz crystaltuning fork resonator and the oscillation frequency of the fundamentalmode of vibration thereof is about 32.768 kHz with a frequency deviationwithin a range of −100 ppm to +100 ppm.
 13. An electronic apparatusaccording to claim 11; wherein the quartz crystal tuning fork resonatorhas a merit value M₁ of the fundamental mode of vibration, the meritvalue M, being defined by the ratio (Q₁/r₁); wherein the dimension ofeach of the quartz crystal tuning fork shape, the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines and the electrodedisposed on the at least one of the first and second surfaces of the atleast one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines is determined so that the merit value M₁ of the fundamental modeof vibration of the quartz crystal tuning fork resonator is greater thanthe merit value M₂ of the second overtone mode of vibration thereof, andthe capacitance ratio r₂ of the second overtone mode of vibrationthereof is greater than 1500; wherein the opposite main surfaces have afirst main surface and a second main surface; and wherein the at leastone groove comprises a groove formed in at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines so that a width of the groove formed in the at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is less than a spaced-apartdistance between the first and second quartz crystal tuning fork tines,and a length of the groove formed in the at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is less than 1.29 mm.
 14. An electronic apparatusaccording to claim 13; wherein each of the first and second quartzcrystal tuning fork tines has a width; wherein the width of each of thefirst and second quartz crystal tuning fork tines is greater than 0.05mm and less than 0.1 mm; wherein a distance in the width direction ofthe groove measured from an outer edge of the groove to an outer edge ofthe corresponding one of the first and second quartz crystal tuning forktines is less than 0.015 mm; wherein the quartz crystal tuning forkresonator has an overall length within a range of 1.2 mm to 2 mm; andwherein the quartz crystal tuning fork base has a length less than 0.5mm.
 15. An electronic apparatus according to claim 14; wherein thequartz crystal tuning fork base has a first base portion including afirst width W₅ and a second base portion including a second width W₆ sothat two cut portions are formed between the first and second baseportions of the quartz crystal tuning fork base, each of the first andsecond quartz crystal tuning fork tines being connected to the firstbase portion of the quartz crystal tuning fork base; wherein the secondbase portion of the quartz crystal tuning fork base has a length 1₄within a range of 0.05 mm to 0.3 mm, and a first side surface and asecond side surface opposite the first side surface; wherein a firstframe is connected to the first side surface of the second base portionof the quartz crystal tuning fork base and a second frame is connectedto the second side surface of the second base portion of the quartzcrystal tuning fork base so that each of the first and second framesextends in a common direction with the first and second quartz crystaltuning fork tines outside the first and second quartz crystal tuningfork tines; wherein the case is a ceramics case having an interior spaceand first and second mounting portions in the interior space; whereinthe first frame is mounted on the first mounting portion in the interiorspace of the ceramics case by a first adhesive and the second frame ismounted on the second mounting portion in the interior space of theceramics case by a second adhesive; wherein a first electrode isdisposed on a surface of each of the first and second frames and asecond electrode is disposed on a surface of each of the first andsecond mounting portions in the interior space of the ceramics case;wherein the first electrode disposed on the surface of the first frameis connected to the second electrode disposed on the surface of thefirst mounting portion in the interior space of the ceramics casethrough the first adhesive and the first electrode disposed on thesurface of the second frame is connected to the second electrodedisposed on the surface of the second mounting portion in the interiorspace of the ceramics case through the second adhesive; wherein the lidis a metal lid or a glass lid; wherein the metal lid or the glass lid isconnected to the ceramics case to cover an open end of the ceramicscase; and wherein the clock signal for use in operation of theelectronic apparatus to display time information at the display portionhas an oscillation frequency of the fundamental mode of vibration of thequartz crystal tuning fork resonator and the oscillation frequency ofthe fundamental mode of vibration thereof is about 32.768 kHz with afrequency deviation within a range of −100 ppm to +100 ppm.
 16. Anelectronic apparatus according to claim 11; wherein the quartz crystaltuning fork resonator has a merit value M₁ of the fundamental mode ofvibration, the merit value M₁ being defined by the ratio (Q₁/r₁);wherein the dimension of each of the quartz crystal tuning fork shape,the at least one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines and the electrode disposed on the at least one of the first andsecond surfaces of the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines is determined so that the merit value M_(I) ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is greater than 65 and the capacitance ratio r₂ of the secondovertone mode of vibration thereof is greater than 1500, and the qualityfactor Q₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than the quality factor Q₂ of the secondovertone mode of vibration thereof; wherein the opposite main surfaceshave a first main surface and a second main surface; wherein the atleast one groove comprises a groove formed in at least one of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines so that a width of the groove formed in the at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is less than a spaced-apartdistance between the first and second quartz crystal tuning fork tinesand a length of the groove formed in the at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is less than 1.29 mm; wherein the case has an interiorspace and a mounting portion in the interior space; wherein the lid is ametal lid or a glass lid; wherein the metal lid or the glass lid isconnected to the case to cover an open end of the case; and wherein theclock signal for use in operation of the electronic apparatus to displaytime information at the display portion has an oscillation frequency ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator and the oscillation frequency of the fundamental mode ofvibration thereof is about 32.768 kHz with a frequency deviation withina range of −100 ppm to +100 ppm.
 17. An electronic apparatus accordingto claim 11; wherein the dimension of each of the quartz crystal tuningfork shape, the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines and the electrode disposed on the at least one of thefirst and second surfaces of the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines is determined so that the qualityfactor Q₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than the quality factor Q₂ of the secondovertone mode of vibration thereof; wherein the opposite main surfaceshave a first main surface and a second main surface; wherein the atleast one groove comprises a groove formed in at least one of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines so that a width of the groove formed in the at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is less than a spaced-apartdistance between the first and second quartz crystal tuning fork tines,and a length of the groove formed in the at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is less than 1.29 mm; wherein the case has an interiorspace and a mounting portion in the interior space; wherein the lid is ametal lid or a glass lid; wherein the quartz crystal tuning forkresonator is mounted on the mounting portion in the interior space ofthe case; wherein the metal lid or the glass lid is connected to thecase to cover an open end of the case in a vacuum; and wherein the clocksignal for use in operation of the electronic apparatus to display timeinformation at the display portion has an oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator and the oscillation frequency of the fundamental mode ofvibration thereof is about 32.768 kHz with a frequency deviation withina range of −100 ppm to +100 ppm.
 18. An electronic apparatus accordingto claim 11; wherein the first quartz crystal oscillating circuitcomprises an amplification circuit having the first amplifier and afeedback circuit having the first capacitors and the first quartzcrystal unit including the quartz crystal tuning fork resonator; whereinthe amplification circuit of the first quartz crystal oscillatingcircuit has a negative resistance −RL₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator and a negativeresistance −RL₂ of the second overtone mode of vibration thereof, |−RL₁|representing the absolute value of the negative resistance −RL₁ and|−RL₂| representing the absolute value of the negative resistance −RL₂;wherein the quartz crystal tuning fork resonator has an angularfrequency ω₁ of the fundamental mode of vibration and an angularfrequency ω₂ of the second overtone mode of vibration; wherein a risetime t_(r1) of the fundamental mode of vibration of the quartz crystaltuning fork resonator in the first quartz crystal oscillating circuit isdefined by t_(r1)=kQ₁/(ω₁(−1+ |−RL₁|/R₁)) and a rise time t_(r2) of thesecond overtone mode of vibration of the quartz crystal tuning forkresonator therein is defined by t_(r2)=kQ₂/(ω₂(−1+|RL₂|/R₂)), where k isa constant value; and wherein each of |−RL₁|, |RL₂| and the dimension ofeach of the quartz crystal tuning fork shape, the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines and the electrodedisposed on the at least one of the first and second surfaces of the atleast one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines is determined so that the rise time t_(r1) of the fundamental modeof vibration of the quartz crystal tuning fork resonator is less thanthe rise time t_(r2) of the second overtone mode of vibration thereof.19. An electronic apparatus according to claim 10; wherein the dimensionof each of the quartz crystal tuning fork shape, the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines and the electrodedisposed on the at least one of the first and second surfaces of the atleast one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines is determined so that the capacitance ratio r₁ of the fundamentalmode of vibration of the quartz crystal tuning fork resonator is lessthan the capacitance ratio r₂ of the second overtone mode of vibrationthereof.
 20. An electronic apparatus according to claim 19; wherein thequartz crystal tuning fork resonator has a merit value M₁ of thefundamental mode of vibration, the merit value M₁ being defined by theratio (Q₁/r₁); wherein the dimension of each of the quartz crystaltuning fork shape, the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines and the electrode disposed on the at least oneof the first and second surfaces of the at least one groove formed inthe at least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines is determined so that the meritvalue M₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is greater than 65 and the capacitance ratio r₂ ofthe second overtone mode of vibration thereof is greater than 1500;wherein a spaced-apart distance between the first and second quartzcrystal tuning fork tines is in the range of 0.05 mm to 0.35 mm; whereinthe opposite main surfaces have a first main surface and a second mainsurface, each of the first and second main surfaces of each of the firstand second quartz crystal tuning fork tines having a central linearportion; wherein the quartz crystal tuning fork resonator has an overalllength, and a series resistance R₁ of the fundamental mode of vibrationand a series resistance R₂ of the second overtone mode of vibration;wherein the at least one groove comprises a groove having a lengthformed in the central linear portion of each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines so that a width of the groove formed in the central linear portionof each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is in the range of 0.03 mm to0.12 mm and less than the spaced-apart distance between the first andsecond quartz crystal tuning fork tines, and a length of the grooveformed in the central linear portion of each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is within a range of 20% to 78% of the overall length of thequartz crystal tuning fork resonator and less than 1.29 mm; wherein eachof the length of the groove formed in the central linear portion of eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines and the overall length of the quartzcrystal tuning fork resonator is determined so that R₁ is less than0.86R₂; wherein the case is a ceramics case having an interior space anda mounting portion in the interior space, and a through-hole; whereinthe lid is a metal lid or a glass lid; wherein the quartz crystal tuningfork base has a first base portion including a first width W₅ and asecond base portion including a second width W₆ greater than or equal tothe first width W₅ so that two cut portions are formed between the firstand second base portions of the quartz crystal tuning fork base, each ofthe first and second quartz crystal tuning fork tines being connected tothe first base portion of the quartz crystal tuning fork base; whereinthe second base portion of the quartz crystal tuning fork base ismounted on the mounting portion in the interior space of the ceramicscase by a conductive adhesive; wherein the metal lid or the glass lid isconnected to the ceramics case to cover an open end of the ceramicscase; wherein a metal or a glass is disposed in the through-hole of theceramics case to close the through-hole thereof in a vacuum; and whereinthe clock signal for use in operation of the electronic apparatus todisplay time information at the display portion has an oscillationfrequency of the fundamental mode of vibration of the quartz crystaltuning fork resonator and the oscillation frequency of the fundamentalmode of vibration thereof is about 32.768 kHz with a frequency deviationwithin a range of −100 ppm to +100 ppm.
 21. An electronic apparatusaccording to claim 20; wherein the groove is formed in the centrallinear portion of each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines so that theoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator comprises a first preselected oscillationfrequency and a turning point of the quartz crystal tuning forkresonator is in the range of 15° C. to 35° C.; wherein a metal film isformed on at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines so that theoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator comprises a second preselected oscillationfrequency; wherein the metal film formed on the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines is trimmed so that the oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator comprises a third preselected oscillation frequency; andwherein the oscillation frequency of the fundamental mode of vibrationof the quartz crystal tuning fork resonator is adjusted so that theoscillation frequency of the fundamental mode of vibration thereofcomprises a fourth preselected oscillation frequency.
 22. An electronicapparatus according to claim 21; wherein the groove formed in thecentral linear portion of each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines has a baseportion; wherein the groove is formed in the central linear portion ofeach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a thickness of the baseportion of the groove formed in the central linear portion of each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is less than 0.05 mm and the firstpreselected oscillation frequency is in the range of 32.78 kHz to 34.4kHz; wherein the second preselected oscillation frequency is lower than32.73 kHz; wherein the third preselected oscillation frequency is about32.768 kHz with a frequency deviation within a range of −9000 ppm to+5000 ppm; and wherein the fourth preselected oscillation frequency isabout 32.768 kHz with a frequency deviation within a range of −100 ppmto +100 ppm.
 23. An electronic apparatus according to claim 22; whereinthe metal film formed on the at least one of the opposite main surfacesof each of the first and second quartz crystal tuning fork tines istrimmed in a quartz crystal wafer using a laser so that the oscillationfrequency of the fundamental mode of vibration of the quartz crystaltuning fork resonator comprises a fifth preselected oscillationfrequency; and wherein the fifth preselected oscillation frequency isabout 32.768 kHz with a frequency deviation within a range of −9000 ppmto +100 ppm.
 24. An electronic apparatus according to claim 19; whereinthe quartz crystal tuning fork resonator has a merit value M_(I) of thefundamental mode of vibration, the merit value M₁ being defined by theratio (Q₁/r₁); wherein the dimension of each of the quartz crystaltuning fork shape, the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines and the electrode disposed on the at least oneof the first and second surfaces of the at least one groove formed inthe at least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines is determined so that the meritvalue M, of the fundamental mode of vibration of the quartz crystaltuning fork resonator is greater than the merit value M₂ of the secondovertone mode of vibration thereof; wherein the opposite main surfaceshave a first main surface and a second main surfaces; wherein the atleast one groove comprises a groove formed in at least one of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines so that a length of the groove formed in the at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is less than 1.29 mm; whereinthe case is a ceramics case having an interior space and a mountingportion in the interior space; wherein the lid is a metal lid or a glasslid; wherein the quartz crystal tuning fork resonator is mounted on themounting portion in the interior space of the ceramics case; wherein themetal lid or the glass lid is connected to the ceramics case to cover anopen end of the ceramics case; and wherein the clock signal for use inoperation of the electronic apparatus to display time information at thedisplay portion has an oscillation frequency of the fundamental mode ofvibration of the quartz crystal tuning fork resonator and theoscillation frequency of the fundamental mode of vibration thereof isabout 32.768 kHz with a frequency deviation within a range of −100 ppmto +100 ppm.
 25. An electronic apparatus according to claim 24; whereina metal film is formed on at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines so thatthe oscillation frequency of the fundamental mode of vibration of thequartz crystal tuning fork resonator comprises a first preselectedoscillation frequency; wherein the metal film formed on the at least oneof the opposite main surfaces of each of the first and second quartzcrystal tuning fork tines is trimmed so that the oscillation frequencyof the fundamental mode of vibration of the quartz crystal tuning forkresonator comprises a second preselected oscillation frequency; whereinthe oscillation frequency of the fundamental mode of vibration of thequartz crystal tuning fork resonator is adjusted so that the oscillationfrequency of the fundamental mode of vibration thereof comprises a thirdpreselected oscillation frequency; and wherein the groove is formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that the oscillationfrequency of the fundamental mode of vibration of the quartz crystaltuning fork resonator comprises a fourth preselected oscillationfrequency.
 26. An electronic apparatus according to claim 25; whereinthe first preselected oscillation frequency is lower than 32.73 kHz;wherein the second preselected oscillation frequency is about 32.768 kHzwith a frequency deviation within a range of −9000 ppm to +5000 ppm; andwherein the third preselected oscillation frequency is about 32.768 kHzwith a frequency deviation within a range of −100 ppm to +100 ppm. 27.An electronic apparatus according to claim 26; wherein the groove formedin each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines has a base portion; and whereinthe groove is formed in each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so that athickness of the base portion of the groove formed in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines is less than 0.05 mm and the fourth preselectedoscillation frequency is in the range of 32.78 kHz to 34.4 kHz, and aturning point of the quartz crystal tuning fork resonator is in therange of 15° C. to 35° C.
 28. An electronic apparatus according to claim24; wherein the quartz crystal tuning fork resonator is formed in aquartz crystal wafer and has a metal film formed on at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines so that the oscillation frequency of the fundamentalmode of vibration of the quartz crystal tuning fork resonator is greaterthan 31.6 kHz and less than 32.69 kHz; and wherein the metal film formedon the at least one of the opposite main surfaces of each of the firstand second quartz crystal tuning fork tines is trimmed in the quartzcrystal wafer using a laser so that the oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator is about 32.768 kHz with a frequency deviation within a rangeof −9000 ppm to +5000 ppm.
 29. An electronic apparatus according toclaim 10; wherein the quartz crystal tuning fork resonator has a meritvalue M₁ of the fundamental mode of vibration, the merit value M₁ beingdefined by the ratio (Q₁/r₁); wherein the dimension of each of thequartz crystal tuning fork shape, the at least one groove formed in theat least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines and the electrode disposed onthe at least one of the first and second surfaces of the at least onegroove formed in the at least one of the opposite main surfaces of eachof the first and second quartz crystal tuning fork tines is determinedso that the merit value M₁ of the fundamental mode of vibration of thequartz crystal tuning fork resonator is greater than the merit value M₂of the second overtone mode of vibration thereof, and the capacitanceratio r₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than the capacitance ratio r₂ of thesecond overtone mode of vibration thereof and the capacitance ratio r₂of the second overtone mode of vibration thereof is greater than 1500;wherein the opposite main surfaces have a first main surface and asecond main surfaces; wherein the at least one groove comprises a grooveformed in at least one of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines so that a lengthof the groove formed in the at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is less than 1.29 mm; wherein the case is a tubular case havingtwo lead wires; wherein the lid is a metal lid; wherein the quartzcrystal tuning fork base is mounted on the two lead wires of the tubularcase by a solder or a conductive adhesive; wherein the tubular case iscovered by the metal lid in a vacuum; and wherein the clock signal foruse in operation of the electronic apparatus to display time informationat the display portion has an oscillation frequency of the fundamentalmode of vibration of the quartz crystal tuning fork resonator and theoscillation frequency of the fundamental mode of vibration thereof isabout 32.768 kHz with a frequency deviation within a range of −100 ppmto +100 ppm.
 30. An electronic apparatus according to claim 10; whereinthe quartz crystal tuning fork resonator has a merit value M₁ of thefundamental mode of vibration, the merit value M₁ being defined by(Q₁/r₁); wherein the dimension of each of the quartz crystal tuning forkshape, the at least one groove formed in the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines and the electrode disposed on the at least one of thefirst and second surfaces of the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines is determined so that the merit valueM₁ of the fundamental mode of vibration of the quartz crystal tuningfork resonator is greater than 65 and the capacitance ratio r₂ of thesecond overtone mode of vibration thereof is greater than 1500; whereinthe opposite main surfaces have a first main surface and a second mainsurfaces; and wherein the at least one groove comprises a groove formedin at least one of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a length ofthe groove formed in the at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is less than 1.29 mm.
 31. An electronic apparatus according toclaim 10; wherein the quartz crystal tuning fork resonator has a cuttingangle and a piezoelectric constant e′₁₂ to drive the quartz crystaltuning fork resonator; and wherein each of the cutting angle of thequartz crystal tuning fork resonator and the dimension of each of thequartz crystal tuning fork shape, the at least one groove formed in theat least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines and the electrode disposed onthe at least one of the first and second surfaces of the at least onegroove formed in the at least one of the opposite main surfaces of eachof the first and second quartz crystal tuning fork tines is determinedso that the piezoelectric constant e′₁₂ of the quartz crystal tuningfork resonator is in the range of 0.12 C/m² to 0.19 C/m² in the absolutevalue.
 32. An electronic apparatus according to claim 10; wherein thedimension of each of the quartz crystal tuning fork shape, the at leastone groove formed in the at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines and theelectrode disposed on the at least one of the first and second surfacesof the at least one groove formed in the at least one of the oppositemain surfaces of each of the first and second quartz crystal tuning forktines is determined so that the capacitance ratio r₂ of the secondovertone mode of vibration of the quartz crystal tuning fork resonatoris greater than 1500; and wherein the at least one groove is formed inthe at least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of the at leastone groove formed in the at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines is greaterthan or equal to a distance in the width direction of the at least onegroove measured from an outer edge of the first surface of the at leastone groove to an outer edge of the at least one side surface of thecorresponding one of the first and second quartz crystal tuning forktines and a length of the at least one groove formed in the at least oneof the opposite main surfaces of each of the first and second quartzcrystal tuning fork tines is less than 1.29 mm.
 33. An electronicapparatus according to claim 32; wherein the quartz crystal tuning forkresonator has an oscillation frequency of the fundamental mode ofvibration; wherein the at least one groove formed in the at least one ofthe opposite main surfaces of each of the first and second quartzcrystal tuning fork tines has a base portion; wherein the at least onegroove is formed in the at least one of the opposite main surfaces ofeach of the first and second quartz crystal tuning fork tines so that athickness of the base portion of the at least one groove formed in theat least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines is less than 0.05 mm and theoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is in the range of 32.78 kHz to 34.4 kHz,and a turning point of the quartz crystal tuning fork resonator is inthe range of 15° C. to 35° C.; wherein a metal film is formed on atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines so that the oscillation frequency ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is lower than 32.73 kHz; and wherein the metal film formed onthe at least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines is trimmed so that theoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is about 32.768 kHz with a frequencydeviation within a range of −9000 ppm to +5000 ppm.
 34. An electronicapparatus according to claim 10; wherein the opposite main surfaces havea first main surface and a second main surface; wherein the at least onegroove comprises a groove formed in at least one of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines so that a distance in the width direction of the groove measuredfrom an outer edge of the groove to an outer edge of the correspondingone of the first and second quartz crystal tuning fork tines is lessthan 0.015 mm; wherein a length of the groove formed in the at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is less than 1.29 mm; wherein thequartz crystal tuning fork resonator has an overall length less than2.18 mm; and wherein the quartz crystal tuning fork base has a lengthless than 0.5 mm.
 35. An electronic apparatus according to claim 34;wherein the length of the quartz crystal tuning fork base is within arange of 0.12 mm to 0.255 mm or within a range of 0.264 mm to 0.277 mmor within a range of 0.29 mm to 0.48 mm.
 36. An electronic apparatusaccording to claim 10; wherein the quartz crystal tuning fork resonatorhas a merit value M₁ of the fundamental mode of vibration, the meritvalue M₁ being defined by the ratio (Q₁/r₁); wherein the dimension ofeach of the quartz crystal tuning fork shape, the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines and the electrodedisposed on the at least one of the first and second surfaces of the atleast one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines is determined so that the merit value M₁ of the fundamental modeof vibration of the quartz crystal tuning fork resonator is greater than65, and the capacitance ratio r₁ of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is less than the capacitanceratio r₂ of the second overtone mode of vibration thereof; wherein thefirst quartz crystal oscillating circuit comprises an amplificationcircuit having the first amplifier and a feedback circuit having thefirst capacitors and the first quartz crystal unit including the quartzcrystal tuning fork resonator; wherein the amplification circuit of thefirst quartz crystal oscillating circuit has a negative resistance −RL₁of the fundamental mode of vibration of the quartz crystal tuning forkresonator and a negative resistance −RL₂ of the second overtone mode ofvibration thereof, |−RL₁| representing the absolute value of thenegative resistance −RL₁ and |−RL₂| representing the absolute value ofthe negative resistance −RL₂; wherein the quartz crystal tuning forkresonator has an angular frequency ω₁ of the fundamental mode ofvibration and an angular frequency ω₂ of the second overtone mode ofvibration; wherein a rise time t_(r1) of the fundamental mode ofvibration of the quartz crystal tuning fork resonator in the firstquartz crystal oscillating circuit is defined by t_(r1)=kQ₁/(ω₁(−1+|−RL₁|/R₁)) and a rise time t_(r2) of the second overtone mode ofvibration of the quartz crystal tuning fork resonator therein is definedby t_(r2)=kQ₂/(ω₂(−1+ |−RL₂|/R₂)), where k is a constant value; andwherein each of |−RL₁|, |RL₂| and the dimension of each of the quartzcrystal tuning fork shape, the at least one groove formed in the atleast one of the opposite main surfaces of each of the first and secondquartz crystal tuning fork tines and the electrode disposed on the atleast one of the first and second surfaces of the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines is determined so thatthe rise time t_(r1) of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is less than the rise time t_(r2) of thesecond overtone mode of vibration thereof.
 37. An electronic apparatusaccording to claim 36; wherein the quartz crystal tuning fork base has afirst base portion including a first width W₅ and a second base portionincluding a second width W₆ greater than or equal to the first width W₅so that two cut portions are formed between the first and second baseportions of the quartz crystal tuning fork base, each of the first andsecond quartz crystal tuning fork tines being connected to the firstbase portion of the quartz crystal tuning fork base; wherein aspaced-apart distance between the first and second quartz crystal tuningfork tines is in the range of 0.05 mm to 0.35 mm; wherein the quartzcrystal tuning fork resonator has an oscillation frequency of thefundamental mode of vibration; wherein the opposite main surfaces have afirst main surface and a second main surface, each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines having a central linear portion; wherein the at leastone groove comprises a groove having a base portion formed in thecentral linear portion of each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so that awidth of the groove formed in the central linear portion of each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is in the range of 0.03 mm to 0.12 mm and lessthan the spaced-apart distance between the first and second quartzcrystal tuning fork tines, a length of the groove formed in the centrallinear portion of each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is within a rangeof 40% to 80% of a length of each of the first and second quartz crystaltuning fork tines and less than 1.29 mm, a turning point of the quartzcrystal tuning fork resonator is in the range of 15° C. to 35° C., athickness of the base portion of the groove formed in the central linearportion of each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is less than 0.05 mmand the oscillation frequency of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is in the range of 32.78 kHz to34.4 kHz; wherein a metal film is formed on at least one of the oppositemain surfaces of each of the first and second quartz crystal tuning forktines so that the oscillation frequency of the fundamental mode ofvibration of the quartz crystal tuning fork resonator comprises a firstpreselected oscillation frequency; wherein the first preselectedoscillation frequency is greater than 31.6 kHz and less than 32.69 kHz;wherein the metal film formed on the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines is trimmed in a quartz crystal wafer so that the oscillationfrequency of the fundamental mode of vibration of the quartz crystaltuning fork resonator comprises a second preselected oscillationfrequency; wherein the second preselected oscillation frequency is about32.768 kHz with a frequency deviation within a range of −9000 ppm to+5000 ppm; wherein the oscillation frequency of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is adjusted sothat the oscillation frequency of the fundamental mode of vibrationthereof comprises a third preselected oscillation frequency; wherein thethird preselected oscillation frequency is about 32.768 kHz with afrequency deviation within a range of −100 ppm to +100 ppm; wherein thecase is a ceramics case having an interior space and a mounting portionin the interior space, and a through-hole; wherein the quartz crystaltuning fork resonator is mounted on the mounting portion in the interiorspace of the ceramics case; wherein the lid is a metal lid or a glasslid; wherein the metal lid or the glass lid is connected to the ceramicscase to cover an open end of the ceramics case; wherein a metal or aglass is disposed in the through-hole of the ceramics case to close thethrough-hole thereof in a vacuum; and wherein the clock signal for usein operation of the electronic apparatus to display time information atthe display portion has the third preselected oscillation frequency ofabout 32.768 kHz with the frequency deviation within the range of −100ppm to +100 ppm.
 38. An electronic apparatus according to claim 36;wherein a spaced-apart distance between the first and second quartzcrystal tuning fork tines is in the range of 0.05 mm to 0.35 mm; whereinthe quartz crystal tuning fork resonator has an oscillation frequency ofthe fundamental mode of vibration; wherein the opposite main surfaceshave a first main surface and a second main surface; wherein the atleast one groove comprises a groove having a base portion formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a width of the groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is in the range of 0.03 mm to0.12 mm and less than the spaced-apart distance between the first andsecond quartz crystal tuning fork tines, a length of the groove formedin each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is within a range of 30% to 80%of a length of each of the first and second quartz crystal tuning forktines and less than 1.29 mm, a turning point of the quartz crystaltuning fork resonator is in the range of 15° C. to 35° C., a thicknessof the base portion of the groove formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is less than 0.05 mm and the oscillation, frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator is in the range of 32.78 kHz to 34.4 kHz; wherein a metal filmis formed on at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines so that theoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator comprises a first preselected oscillationfrequency; wherein the first preselected oscillation frequency is lowerthan 32.73 kHz; wherein the metal film formed on the at least one of theopposite main surfaces of each of the first and second quartz crystaltuning fork tines is trimmed so that the oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator comprises a second preselected oscillation frequency; whereinthe second preselected oscillation frequency is about 32.768 kHz with afrequency deviation within a range of −9000 ppm to +100 ppm; wherein theoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is adjusted so that the oscillationfrequency of the fundamental mode of vibration thereof comprises a thirdpreselected oscillation frequency; wherein the third preselectedoscillation frequency is about 32.768 kHz with a frequency deviationwithin a range of −100 ppm to +100 ppm; wherein the case is a ceramicscase having an interior space and a mounting portion in the interiorspace; wherein the quartz crystal tuning fork resonator is mounted onthe mounting portion in the interior space of the ceramics case; whereinthe lid is a metal lid or a glass lid; wherein the metal lid or theglass lid is connected to the ceramics case to cover an open end of theceramics case; and wherein the clock signal for use in operation of theelectronic apparatus to display time information at the display portionhas the third preselected oscillation frequency of about 32.768 kHz withthe frequency deviation within the range of −100 ppm to +100 ppm.